{"id":149,"date":"2021-12-25T15:56:05","date_gmt":"2021-12-25T18:56:05","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=149"},"modified":"2024-12-24T14:27:00","modified_gmt":"2024-12-24T17:27:00","slug":"hardy-ramanujan-number-1729-revised","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=149","title":{"rendered":"Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 &#8211; Part 1"},"content":{"rendered":"\n<h3 class=\"wp-block-heading has-text-align-right has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-fc798738aa851d22348a6dbcb8c9cbf3\">137th Birth Anniversary of S. Ramanujan,<br>December 22, 1887-April 26, 1920<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-right has-vivid-purple-color has-text-color has-link-color wp-elements-054c3950117695baa11a47d5eb42c129\">National Mathematics Day, India &#8211; December 22<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Part 1: Recreation of Number on 1729<br>Part 2: <a href=\"https:\/\/numbers-magic.com\/?p=13751\">Magic Square<\/a><\/h3>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-background\" style=\"background:linear-gradient(135deg,rgb(122,220,180) 0%,rgb(255,255,255) 47%,rgb(0,208,130) 100%)\">This paper brings representations of 1729, a famous&nbsp;<strong>Hardy-Ramanujan number<\/strong>&nbsp;in different situations. These representations are of&nbsp;<strong>crazy-type, single digit, single letter, Selfie-type, running expressions, selfie fractions, equivalent fractions, Triangular, Fibonacci, fixed digits repetitions prime numbers patterns , Pythagorean triples, palindromic-type, polygonal-type, prime numbers, embedded, repeated, etc.&nbsp;<\/strong>Ideas toward&nbsp;<strong>magic squares<\/strong>&nbsp;are also extended. Some quotes and historical notes on Ramanujan\u2019s life are also specified.  <\/p>\n\n\n\n<p class=\"has-text-align-justify has-background\" style=\"background:linear-gradient(135deg,rgb(122,220,180) 0%,rgb(255,255,255) 47%,rgb(0,208,130) 100%)\">This work brings <strong>magic squares<\/strong> connected with S. Ramanujan&#8217;s life and with Hardy-Ramanujan number 1729. There are three different types of <strong>magic squares<\/strong>. The <strong>first type<\/strong> is based on some historical years of S. Ramanujan&#8217;s life. The <strong>second type<\/strong> is with magic sum as 1729. In this case the magic squares constructed are of orders 7, 13, 14 and 19. The \\textbf{third type} is magic squares based on <strong>Pythagorean tripes<\/strong> where the number 1729 is one the entry. In this case the magic squares constructed are of orders 6, 7, 11 and 19.  <\/p>\n\n\n\n<p class=\"has-text-align-justify has-background\" style=\"background:linear-gradient(135deg,rgb(122,220,180) 0%,rgb(255,255,255) 47%,rgb(0,208,130) 100%)\">It is revised and extended version of author\u2019s&nbsp;<a href=\"https:\/\/inderjtaneja.com\/2017\/07\/29\/hardy-ramanujan-number-1729-july-29-17\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>previos work.<\/strong><\/a>  Below is a link of this work for download. <\/p>\n\n\n\n<ul style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 42%,rgb(152,150,240) 100%)\" class=\"wp-block-list has-background\">\n<li><strong>Inder J. Taneja<\/strong>, Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729, <strong>Zenodo<\/strong>, December 20, 2024, pp. 1-127, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14538297\">https:\/\/doi.org\/10.5281\/zenodo.14538297<\/a>\n<ul class=\"wp-block-list\">\n<li>Site links:\n<ul class=\"wp-block-list\">\n<li>Part 1:\u00a0<a href=\"https:\/\/inderjtaneja.wordpress.com\/2021\/12\/25\/hardy-ramanujan-number-1729-revised\/\">Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 \u2013 Part 1<\/a>\u00a0(old site)<br>Part 1:\u00a0<a href=\"https:\/\/numbers-magic.com\/?p=149\">Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 \u2013 Part 1<\/a>\u00a0(new site)<\/li>\n\n\n\n<li>Part 2:\u00a0<a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/12\/24\/numbers-and-magic-squares-representations-of-hardy-ramanujan-number-1729-part-2\/\">Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 \u2013 Part 2\u00a0<\/a>(old site)<br>Part 2:\u00a0<a href=\"https:\/\/numbers-magic.com\/?p=13751\">Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 \u2013 Part 2<\/a>\u00a0(new site)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-justify has-background\" style=\"background:linear-gradient(135deg,rgb(122,220,180) 0%,rgb(255,255,255) 47%,rgb(0,208,130) 100%)\">Below are the itens that we worked with representations of the Hardy Ramanujan Number 1729<\/p>\n\n\n\n<ol style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 69%,rgb(255,105,0) 100%)\" class=\"wp-block-list has-background\">\n<li>Magic Squared On Ramanujan&#8217;s Life Numbers<\/li>\n\n\n\n<li>Single Digit Representations and Patterns<\/li>\n\n\n\n<li>Single Letter Representations and Pattern<\/li>\n\n\n\n<li>Crazy and Pyramid-Type Representations<\/li>\n\n\n\n<li>Same Digits Both Sides<\/li>\n\n\n\n<li>Same Digits Power-Plus<\/li>\n\n\n\n<li>Same Digits: Factorial-Power<\/li>\n\n\n\n<li>Narcissistic-Type Representation<\/li>\n\n\n\n<li>Power Representations<\/li>\n\n\n\n<li>Fibonacci Sequence Representation<\/li>\n\n\n\n<li>S-gonal Values<\/li>\n\n\n\n<li>Polygonal Numbers<\/li>\n\n\n\n<li>Selfie-Fractions<\/li>\n\n\n\n<li>Equivalent Fractions<\/li>\n\n\n\n<li>Pythagorean Triples and Patterns<\/li>\n\n\n\n<li>Pandigital-Type Pythagorean Triples<\/li>\n\n\n\n<li>Upside-Down and Mirror Looking<\/li>\n\n\n\n<li>Special Representations<\/li>\n\n\n\n<li>Numbers from 1 to 1729 in Terms of 1729-9271<\/li>\n\n\n\n<li>Running Equality Expressions<\/li>\n\n\n\n<li>Selfie Representations<\/li>\n\n\n\n<li>Fixed Digits Repetitions Prime Patterns<\/li>\n\n\n\n<li>Embedded Palindromic Prime Patterns<\/li>\n\n\n\n<li>Magic Square Type Palprimes<\/li>\n\n\n\n<li>Palindromic Prime Numbers<\/li>\n\n\n\n<li>Two Color Pattern Designs for 17-29<\/li>\n\n\n\n<li>Magic Squares with 1729 &#8211; See second part<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-77acb99e020bdddcde257a0cef3c1d1f\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Single Digit Representations and Patterns<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"566\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-07-2-1024x566.png\" alt=\"\" class=\"wp-image-13676\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-07-2-1024x566.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-07-2-300x166.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-07-2-768x425.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-07-2-535x296.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-07-2.png 1253w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" width=\"1024\" height=\"443\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-08-2-1024x443.png\" alt=\"\" class=\"wp-image-13677\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-08-2-1024x443.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-08-2-300x130.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-08-2-768x332.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-08-2-535x231.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-08-2.png 1248w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-c5ad40a697eac2c63b10e5906a267efe\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Single Letter Representations and Pattern<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" width=\"1024\" height=\"376\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-09-2-1024x376.png\" alt=\"\" class=\"wp-image-13678\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-09-2-1024x376.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-09-2-300x110.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-09-2-768x282.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-09-2-535x197.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-09-2.png 1249w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"573\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-10-2-1024x573.png\" alt=\"\" class=\"wp-image-13679\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-10-2-1024x573.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-10-2-300x168.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-10-2-768x430.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-10-2-535x299.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-10-2.png 1247w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-ce23c7d1168fa5f07a7121a23bd7230e\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Crazy and Pyramid-Type Representations<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"838\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-11a-1024x838.png\" alt=\"\" class=\"wp-image-13680\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-11a-1024x838.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-11a-300x246.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-11a-768x629.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-11a-535x438.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-11a.png 1247w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"693\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-11b-1-1024x693.png\" alt=\"\" class=\"wp-image-13743\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-11b-1-1024x693.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-11b-1-300x203.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-11b-1-768x520.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-11b-1-535x362.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-11b-1.png 1249w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"466\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-12-2-1024x466.png\" alt=\"\" class=\"wp-image-13682\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-12-2-1024x466.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-12-2-300x136.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-12-2-768x349.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-12-2-535x243.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-12-2.png 1249w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"397\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-13-2-1024x397.png\" alt=\"\" class=\"wp-image-13683\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-13-2-1024x397.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-13-2-300x116.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-13-2-768x298.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-13-2-535x207.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-13-2.png 1248w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"499\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-14-2-1024x499.png\" alt=\"\" class=\"wp-image-13684\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-14-2-1024x499.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-14-2-300x146.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-14-2-768x374.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-14-2-535x261.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-14-2.png 1248w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"631\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-15-2-1024x631.png\" alt=\"\" class=\"wp-image-13685\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-15-2-1024x631.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-15-2-300x185.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-15-2-768x473.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-15-2-535x329.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-15-2.png 1247w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-bec6d3c1a2bc47475779a5dcfb013f2f\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Same Digits Both Sides<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"682\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-16-2-1024x682.png\" alt=\"\" class=\"wp-image-13687\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-16-2-1024x682.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-16-2-300x200.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-16-2-768x512.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-16-2-535x357.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-16-2.png 1250w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-0344081f23cd2f71e8a94e6fdcbc5b68\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Same Digits Power-Plus<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"598\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-17-2-1024x598.png\" alt=\"\" class=\"wp-image-13686\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-17-2-1024x598.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-17-2-300x175.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-17-2-768x448.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-17-2-535x312.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-17-2.png 1252w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"930\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-18-2-1024x930.png\" alt=\"\" class=\"wp-image-13688\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-18-2-1024x930.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-18-2-300x273.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-18-2-768x698.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-18-2-535x486.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-18-2.png 1248w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-54edf8e4c9f5337d03768728951a38df\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Same Digits: Factorial-Power<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"860\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-19-2-1024x860.png\" alt=\"\" class=\"wp-image-13689\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-19-2-1024x860.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-19-2-300x252.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-19-2-768x645.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-19-2-535x449.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-19-2.png 1249w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-6f27ff00b714f27cf9c4a54a163313a9\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Narcissistic-Type Representation<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"308\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-20-2-1024x308.png\" alt=\"\" class=\"wp-image-13690\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-20-2-1024x308.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-20-2-300x90.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-20-2-768x231.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-20-2-535x161.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-20-2.png 1248w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-7b8ae09b9b5e889cdc883eb15d02513e\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Power Representations<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"964\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-21-2-1024x964.png\" alt=\"\" class=\"wp-image-13691\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-21-2-1024x964.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-21-2-300x282.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-21-2-768x723.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-21-2-535x504.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-21-2.png 1247w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"858\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-22-2-1024x858.png\" alt=\"\" class=\"wp-image-13692\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-22-2-1024x858.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-22-2-300x251.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-22-2-768x643.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-22-2-535x448.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-22-2.png 1250w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"995\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-23-2-995x1024.png\" alt=\"\" class=\"wp-image-13694\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-23-2-995x1024.png 995w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-23-2-292x300.png 292w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-23-2-768x790.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-23-2-535x550.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-23-2.png 1247w\" sizes=\"(max-width: 995px) 100vw, 995px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-9cd4ef35a2305b7c81d4de8244b4f16a\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Fibonacci Sequence Representation<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"412\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-24-2-1024x412.png\" alt=\"\" class=\"wp-image-13695\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-24-2-1024x412.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-24-2-300x121.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-24-2-768x309.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-24-2-535x215.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-24-2.png 1245w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">S-gonal Values<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"868\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-25-2-868x1024.png\" alt=\"\" class=\"wp-image-13693\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-25-2-868x1024.png 868w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-25-2-254x300.png 254w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-25-2-768x906.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-25-2-535x631.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-25-2.png 1249w\" sizes=\"(max-width: 868px) 100vw, 868px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-352d9d6353efa5aa4fd300af1553ad91\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Polygonal Numbers<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"798\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-26-2-1024x798.png\" alt=\"\" class=\"wp-image-13696\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-26-2-1024x798.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-26-2-300x234.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-26-2-768x598.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-26-2-535x417.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-26-2.png 1248w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"798\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-26-3-1024x798.png\" alt=\"\" class=\"wp-image-13697\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-26-3-1024x798.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-26-3-300x234.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-26-3-768x598.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-26-3-535x417.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-26-3.png 1248w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"891\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-27-2-891x1024.png\" alt=\"\" class=\"wp-image-13698\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-27-2-891x1024.png 891w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-27-2-261x300.png 261w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-27-2-768x883.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-27-2-535x615.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-27-2.png 1246w\" sizes=\"(max-width: 891px) 100vw, 891px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"885\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-28-2-1024x885.png\" alt=\"\" class=\"wp-image-13700\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-28-2-1024x885.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-28-2-300x259.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-28-2-768x663.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-28-2-535x462.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-28-2.png 1249w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"948\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-29-2-1024x948.png\" alt=\"\" class=\"wp-image-13701\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-29-2-1024x948.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-29-2-300x278.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-29-2-768x711.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-29-2-535x495.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-29-2.png 1250w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-4cec6026cd9b73c54c095f9708bfe5b8\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Selfie-Fractions<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"502\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-30-2-1024x502.png\" alt=\"\" class=\"wp-image-13702\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-30-2-1024x502.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-30-2-300x147.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-30-2-768x376.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-30-2-535x262.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-30-2.png 1249w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"674\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-31-2-1024x674.png\" alt=\"\" class=\"wp-image-13704\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-31-2-1024x674.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-31-2-300x198.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-31-2-768x506.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-31-2-535x352.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-31-2.png 1248w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"420\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-32-2-1024x420.png\" alt=\"\" class=\"wp-image-13703\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-32-2-1024x420.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-32-2-300x123.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-32-2-768x315.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-32-2-535x220.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-32-2.png 1250w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-12859e30692cd20c796695036bbaec32\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Equivalent Fractions<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"923\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-33-2-1024x923.png\" alt=\"\" class=\"wp-image-13705\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-33-2-1024x923.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-33-2-300x270.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-33-2-768x692.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-33-2-535x482.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-33-2.png 1251w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"898\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-34-4-1024x898.png\" alt=\"\" class=\"wp-image-13706\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-34-4-1024x898.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-34-4-300x263.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-34-4-768x673.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-34-4-535x469.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-34-4.png 1249w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"931\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-35-2-1024x931.png\" alt=\"\" class=\"wp-image-13707\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-35-2-1024x931.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-35-2-300x273.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-35-2-768x698.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-35-2-535x486.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-35-2.png 1250w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-2da9bf2f5da625c8fff37dc4235f3475\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Pythagorean Triples and Patterns<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"488\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-36-2-1024x488.png\" alt=\"\" class=\"wp-image-13708\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-36-2-1024x488.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-36-2-300x143.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-36-2-768x366.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-36-2-535x255.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-36-2.png 1248w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"418\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-37-2-1024x418.png\" alt=\"\" class=\"wp-image-13709\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-37-2-1024x418.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-37-2-300x122.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-37-2-768x314.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-37-2-535x218.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-37-2.png 1249w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"990\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-38-2-990x1024.png\" alt=\"\" class=\"wp-image-13710\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-38-2-990x1024.png 990w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-38-2-290x300.png 290w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-38-2-768x794.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-38-2-535x553.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-38-2.png 1249w\" sizes=\"(max-width: 990px) 100vw, 990px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"655\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-40-2-1024x655.png\" alt=\"\" class=\"wp-image-13713\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-40-2-1024x655.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-40-2-300x192.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-40-2-768x491.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-40-2-535x342.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-40-2.png 1249w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-ae3f13571a5b7755013bb971e346f84b\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Pandigital-Type Pythagorean Triples<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"981\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-41-2-981x1024.png\" alt=\"\" class=\"wp-image-13714\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-41-2-981x1024.png 981w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-41-2-287x300.png 287w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-41-2-768x802.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-41-2-535x558.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-41-2.png 1253w\" sizes=\"(max-width: 981px) 100vw, 981px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-2eaf7b8432dacb6b25a23db5af5701fc\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Upside-Down and Mirror Looking<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"952\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-42-2-1024x952.png\" alt=\"\" class=\"wp-image-13715\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-42-2-1024x952.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-42-2-300x279.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-42-2-768x714.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-42-2-535x497.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-42-2.png 1249w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-2ec86adf926dc89dc247d43dd07c940a\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Special Representations<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"676\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-43-2-1024x676.png\" alt=\"\" class=\"wp-image-13716\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-43-2-1024x676.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-43-2-300x198.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-43-2-768x507.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-43-2-535x353.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-43-2.png 1246w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"936\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-01a-1024x936.png\" alt=\"\" class=\"wp-image-13741\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-01a-1024x936.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-01a-300x274.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-01a-768x702.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-01a-535x489.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-01a.png 1252w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"912\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-01b-1024x912.png\" alt=\"\" class=\"wp-image-13742\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-01b-1024x912.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-01b-300x267.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-01b-768x684.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-01b-535x477.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-01b.png 1255w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-42cc060274a041b4f0879c7e6b9b0fab\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Numbers from 1 to 1729 in Terms of 1729-9271<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"629\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-44-2-1024x629.png\" alt=\"\" class=\"wp-image-13718\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-44-2-1024x629.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-44-2-300x184.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-44-2-768x471.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-44-2-535x328.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-44-2.png 1248w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-df9902001a1352573a7303cbc25c6dd0\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Running Equality Expressions<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"796\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-45-2-1024x796.png\" alt=\"\" class=\"wp-image-13719\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-45-2-1024x796.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-45-2-300x233.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-45-2-768x597.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-45-2-535x416.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-45-2.png 1251w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-019d8e0cc956872769b031ac7f5410c9\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Selfie Representations<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"507\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-46-2-1024x507.png\" alt=\"\" class=\"wp-image-13720\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-46-2-1024x507.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-46-2-300x149.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-46-2-768x381.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-46-2-535x265.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-46-2.png 1251w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"833\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-47-2-833x1024.png\" alt=\"\" class=\"wp-image-13721\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-47-2-833x1024.png 833w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-47-2-244x300.png 244w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-47-2-768x944.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-47-2-535x658.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-47-2-1250x1536.png 1250w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-47-2.png 1252w\" sizes=\"(max-width: 833px) 100vw, 833px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-748209a3f119b0d32aec7a50de2f3b66\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Fixed Digits Repetitions Prime Patterns<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"872\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-48-2-872x1024.png\" alt=\"\" class=\"wp-image-13722\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-48-2-872x1024.png 872w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-48-2-255x300.png 255w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-48-2-768x902.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-48-2-535x628.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-48-2.png 1251w\" sizes=\"(max-width: 872px) 100vw, 872px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"872\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-49-2-872x1024.png\" alt=\"\" class=\"wp-image-13723\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-49-2-872x1024.png 872w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-49-2-256x300.png 256w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-49-2-768x902.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-49-2-535x628.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-49-2.png 1252w\" sizes=\"(max-width: 872px) 100vw, 872px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"870\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-50-2-870x1024.png\" alt=\"\" class=\"wp-image-13725\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-50-2-870x1024.png 870w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-50-2-255x300.png 255w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-50-2-768x904.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-50-2-535x630.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-50-2.png 1250w\" sizes=\"(max-width: 870px) 100vw, 870px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"993\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-51-2-993x1024.png\" alt=\"\" class=\"wp-image-13724\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-51-2-993x1024.png 993w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-51-2-291x300.png 291w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-51-2-768x792.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-51-2-535x552.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-51-2.png 1250w\" sizes=\"(max-width: 993px) 100vw, 993px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"777\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-51b-1024x777.png\" alt=\"\" class=\"wp-image-13726\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-51b-1024x777.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-51b-300x228.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-51b-768x583.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-51b-535x406.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-51b.png 1248w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"777\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-52-2-1024x777.png\" alt=\"\" class=\"wp-image-13727\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-52-2-1024x777.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-52-2-300x228.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-52-2-768x583.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-52-2-535x406.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-52-2.png 1248w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-4c1724047cca9644f5ea2b9facf41d34\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Embedded Palindromic Prime Patterns<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"861\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-53a-1024x861.png\" alt=\"\" class=\"wp-image-13728\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-53a-1024x861.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-53a-300x252.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-53a-768x645.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-53a-535x450.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-53a.png 1247w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"932\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-53b-932x1024.png\" alt=\"\" class=\"wp-image-13729\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-53b-932x1024.png 932w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-53b-273x300.png 273w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-53b-768x843.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-53b-535x588.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-53b.png 1253w\" sizes=\"(max-width: 932px) 100vw, 932px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1006\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-54-2-1006x1024.png\" alt=\"\" class=\"wp-image-13730\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-54-2-1006x1024.png 1006w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-54-2-295x300.png 295w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-54-2-768x782.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-54-2-535x544.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-54-2.png 1249w\" sizes=\"(max-width: 1006px) 100vw, 1006px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"969\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-55-2-969x1024.png\" alt=\"\" class=\"wp-image-13731\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-55-2-969x1024.png 969w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-55-2-284x300.png 284w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-55-2-768x812.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-55-2-535x565.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-55-2.png 1248w\" sizes=\"(max-width: 969px) 100vw, 969px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-db735df564af1d59d05392688eb24277\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Magic Square Type Palprimes<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"699\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-56-2-1024x699.png\" alt=\"\" class=\"wp-image-13732\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-56-2-1024x699.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-56-2-300x205.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-56-2-768x524.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-56-2-535x365.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-56-2.png 1249w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Palindromic Prime Numbers<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"709\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-57-2-1024x709.png\" alt=\"\" class=\"wp-image-13733\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-57-2-1024x709.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-57-2-300x208.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-57-2-768x532.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-57-2-535x371.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-57-2.png 1249w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"370\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-58-2-1024x370.png\" alt=\"\" class=\"wp-image-13734\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-58-2-1024x370.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-58-2-300x108.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-58-2-768x277.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-58-2-535x193.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-58-2.png 1249w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"998\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-59-2-1024x998.png\" alt=\"\" class=\"wp-image-13735\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-59-2-1024x998.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-59-2-300x292.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-59-2-768x748.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-59-2-535x521.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-59-2.png 1249w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"861\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-60-2-1024x861.png\" alt=\"\" class=\"wp-image-13736\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-60-2-1024x861.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-60-2-300x252.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-60-2-768x646.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-60-2-535x450.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-60-2.png 1248w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"793\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-61-2-1024x793.png\" alt=\"\" class=\"wp-image-13737\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-61-2-1024x793.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-61-2-300x232.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-61-2-768x595.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-61-2-535x414.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-61-2.png 1250w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-amber-color has-text-color has-background has-link-color wp-elements-215efa38e2346c23845d11f1c93fb06e\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Two Color Pattern Designs for 17-29<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"672\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-62-2-1024x672.png\" alt=\"\" class=\"wp-image-13738\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-62-2-1024x672.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-62-2-300x197.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-62-2-768x504.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-62-2-535x351.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-62-2.png 1245w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"671\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-63-2-1024x671.png\" alt=\"\" class=\"wp-image-13739\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-63-2-1024x671.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-63-2-300x197.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-63-2-768x503.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-63-2-535x351.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-63-2.png 1253w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"672\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-64-2-1024x672.png\" alt=\"\" class=\"wp-image-13740\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-64-2-1024x672.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-64-2-300x197.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-64-2-768x504.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-64-2-535x351.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-64-2.png 1250w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading has-text-align-center\">References<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>, 2019 In Numbers, <strong>Zenodo<\/strong>, December 31, 2019, pp. 1-27, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.2529103\">http:\/\/doi.org\/10.5281\/zenodo.2529103<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, 2020 In Numbers: Mathematical Style, <strong>Zenodo<\/strong>, December 31, 2019, pp. 1-37, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.3596193\">http:\/\/doi.org\/10.5281\/zenodo.3596193<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, 21 Mathematical Highlights for 2021, <strong>Zenodo<\/strong>, December 26, 2020, pp. 1-75, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.4394408\">http:\/\/doi.org\/10.5281\/zenodo.4394408<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Hardy-Ramanujan Number \u2013 1729, <strong>Zenodo<\/strong>, December 22, 2021, pp. 1-106, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.5799640\">https:\/\/doi.org\/10.5281\/zenodo.5799640<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Mathematical Beauty of 2022, <strong>Zenodo<\/strong>, December 26, 2021, pp. 1-78, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.5805264\">https:\/\/doi.org\/10.5281\/zenodo.5805264<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, 23 and 2023 in Numbers and Patterns, <strong>Zenodo<\/strong>, December 22, 2022, pp. 1-51, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.7473340\">https:\/\/doi.org\/10.5281\/zenodo.7473340<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Mathematical Representations of the Last Day of the Year 23 Written American Style: 12.31.23 (123123), <strong>Zenodo<\/strong>, December 19, 2023, pp. 1-13, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.10405771\">https:\/\/doi.org\/10.5281\/zenodo.10405771<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Mathematical Aspects of 24 and 2024, <strong>Zenodo<\/strong>, December 19, 2023, pp. 1-40, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.10406530\">https:\/\/doi.org\/10.5281\/zenodo.10406530<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares,&nbsp;<strong>Zenodo<\/strong>, December 20, 2024, pp. 1-94,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.14533193\">https:\/\/doi.org\/10.5281\/zenodo.14533193<\/a>.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Part 2: <a href=\"https:\/\/numbers-magic.com\/?p=13751\">Magic Squares<\/a><\/h3>\n\n\n\n<p><a href=\"https:\/\/numbers-magic.com\/?p=13751\">Please see the second part<\/a><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>137th Birth Anniversary of S. Ramanujan,December 22, 1887-April 26, 1920 National Mathematics Day, India &#8211; December 22 Part 1: Recreation of Number on 1729Part 2: Magic Square This paper brings representations of 1729, a famous&nbsp;Hardy-Ramanujan number&nbsp;in different situations. These representations are of&nbsp;crazy-type, single digit, single letter, Selfie-type, running expressions, selfie fractions, equivalent fractions, Triangular, Fibonacci, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":150,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[7],"tags":[],"class_list":["post-149","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-curiosities"],"jetpack_featured_media_url":"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/1729-01.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/149","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=149"}],"version-history":[{"count":16,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/149\/revisions"}],"predecessor-version":[{"id":13984,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/149\/revisions\/13984"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/150"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=149"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=149"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=149"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}