{"id":6703,"date":"2021-07-08T12:43:52","date_gmt":"2021-07-08T11:43:52","guid":{"rendered":"https:\/\/walkingrandomly.com\/?p=6703"},"modified":"2021-07-08T12:43:52","modified_gmt":"2021-07-08T11:43:52","slug":"carnival-of-mathematics-194","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=6703","title":{"rendered":"Carnival of mathematics #194"},"content":{"rendered":"

Welcome to the 194th Carnival of Mathematics<\/a>!\u00a0 I am extremely late in posting this…so late in fact that the 195th edition<\/a> as already been published!<\/p>\n

194 has a few interesting properties.\u00a0 According to its wikipedia entry<\/a>,\u00a0194 is an odious number<\/a>\u00a0that is also the smallest\u00a0Markov number<\/a>\u00a0that is neither a\u00a0Fibonacci number<\/a>\u00a0nor a\u00a0Pell number<\/a>. It’s\u00a0\u00a0the smallest number that can be written as the sum of three\u00a0squares<\/a>\u00a0in five ways and\u00a0is the number of\u00a0irreducible representations<\/a>\u00a0of the\u00a0Monster group<\/a>.<\/p>\n

Micro Visual Proofs – Animated proofs without words<\/strong><\/p>\n

Proofs without words<\/a> have been around for a long time. Diagrams that demonstrate that a mathematical statement is ‘obviously’ true.\u00a0 The example that always springs to my mind is the one below that demonstrates that the sum of consecutive odd numbers is a square number.<\/p>\n

<\/p>\n

Such things have appeared in print for years.\u00a0 The books by Nelsen<\/a> are a wonderful source of many of them and the Mathematical Association of America has a few very nice interactive examples<\/a>.<\/p>\n

Tom Edgar has been working on videos that animate proofs without words for a new YouTube channel called Micro Visual Proofs<\/a> and submitted the one below for this month’s Carnival of math.<\/p>\n