Merry Christmas everyone! It turns out that today is the 360th day of the year, and today’s date is 1225. That means there’s a lot of interesting number facts to go along with!

First off, 1225 is a square number. That’s somewhat interesting on its own (1225 = 35²), but there’s more! Although you’ve probably heard of square numbers, there are triangular numbers, hexagonal numbers, and even more numbers rooted in geometry that might not immediately come to mind.

Looking at 1225, we see that besides being a square number, it’s also a triangular number and a hexagonal number. Not only is it all three, it’s the smallest number (that’s not 1) that can form all three shapes!

Note: You might notice that the “hexagonal numbers” aren’t centered, and instead start from one common point on the side. The numbers related to hexagons that share a center are called the “centered hexagonal numbers”.

Today is also the 360th day of the year. There’s a lot to say about the number 360. One tidbit that doesn’t need a lot of explaining, however, is that 360 is the smallest number divisible by all numbers 1-10 except for 7. A quick way to see this:

360 = 2 × 2 × 2 × 3 × 3 × 5

When looking at the factors of 360, we can find 2, 3, and 5 right away. When we multiply the twos, threes, and fives together, we can find the remaining 4, 6, 8, and 10. Another fun coincidence is that there are 72 primes less than 360, and a factor of 360 is 72.

What an interesting pair of numbers!