HAPPY NEW YEAR 2025!
There was a lot to put into one comic and I couldn't compress the graphs anymore without some of the lines disappearing on me or unless I was willing to dealing with a lot of pixelation. Since I had a lot of shading to do, I did not want the pixelation.
Besides, I wanted you to see all 2,025 of those wonderful little colored boxes!
The funny part is that I had an illustration in a math journal I kept more than a dozen years ago that I wanted to use. The problem was that the page, which was more than 45 boxes tall was not 45 boxes wide. It was a little more than 36, so I had an 36 by 36 square and everything in the comic about was there, but based on the smaller number.
So I recreated it from scratch.
Now, since 2025 is a a perfect square, and the only one that I'll see in my lifetime, until I live until 2116, another 91 years from now, there are a lot of fun facts because it is a perfect square. For one thing, squares are always the sum of two consecutive triangular numbers. Think about splitting a square along the diagonal, but instead, make steps. One triangular number will be one less than the other. Moreover, if you eliminate the center square, you can split the rest of the square into four congruent rectangles, each of which can be divided into two equal triangular numbers. So you'll have 8N + 1, where N is a triangular number.
Finally, N to the second power can always be represented by the sum of the first N consecutive odd numbers.
The bonus to all this is that 45 is itself a triangular number, being the sum of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9, so that just allows even more number play to occur. And though it seems like the oddest coincidence that (1 + 2 + 3 + ... + n)2 will always equal 13 + 23 + 33 + ... + n3
Enjoy the New Year! It should be wonderfully mathematical!
I also write Fiction!The NEW COLLECTION IS AVIALABLE! A Bucket Full of Moonlight, written by Christopher J. Burke, contains 30+ pieces of short stories and flash fiction. It's available from eSpec Books! Order the softcover or ebook at Amazon. Vampires, werewolves, angels, demons, used-car salesmen, fairies, superheroes, space and time travel, and little gray aliens talking to rock creatures and living plants. |
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| My older books include my Burke's Lore Briefs series and In A Flash 2020. |  |
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