Mathematical Beauty

I post mathematical beauty prompts on twitter and include them here for reference. This started as part of an online collaboration with the CMC and NCTM throughout the month of May (2020) but has continued naturally because I enjoying finding and sharing these mathematical gems. In some cases you can click the picture to go to the link.

Before presenting these prompts, I’d like to take a moment to mention one of the most surprising and intriguing results I have come across. The result is contained in the appendices of my book, but I made a huge error in not referencing Harlan Brothers (@HarlanBrothers) for his discovery. This is clearly unacceptable, but I was so incredibly appreciative of his genuine kindness in this matter. I’ve linked his short article here, and have provided the result below. Enjoy!

If we let P(n) denote the product of the elements in the nth row of Pascal’s triangle, then: