## Math Teachers at Play 65: Teach, Learn and Enjoy

Welcome to the 65th edition of Math Teachers at Play. First let us have some trivia about 65. First, 65 is the smallest integer that can be expressed as the sum of two distinct positive squares in two ways 65 = 82 + 12 = 72 + 42. Second, 65 is the length of the hypotenuse of 4 different Pythagorean Triangles:  652 = 162 + 632 = 332 + 562 = 392 + 522 = 252 + 602. Third, 65=15+24+33+42+51. Lastly, 65 is the traditional age for retirement in the United States, the United Kingdom, and other countries including my beloved Philippines.

And now, let the math carnival begin!

Math Teachers at Play 65 Entries

Ing shares how she prepares her 5-year old to before studying preschool elementary. I really like her activity on Number Bonds in her blog Inspirations. Given a shape made of straight lines, can you fold a piece of paper that you can cut out the shape with one straight line? This is Bowman Dickson’s One Cut Problem in his blog Bowman in Arabia. » Read more

## Math Teachers at Play 61

Researching 61 as a number tells us it’s not just prime, but is a twin prime, a cuban prime, the 9th Mersenne prime exponent, and a Pillai prime. That’s primo prime pedigree. It’s a Keith number and thrice Fortunate. (Fortunate numbers are pretty interesting and the subject of an open conjecture.) It’s a centered square number (1+4+8+12+16+20), a centered hexagonal number (1+6+12+18+24) and a centered decagonal number (1+10+20+30); mostly because it’s neighbor 60 is so nice. (Did you see the 60th Math Teachers at Play?) Is there a reason that ∑4n, ∑6n and ∑10n overlap at 60? But the fact that really caught my eye was that 61 is an Euler Zig Zag number. How cool can a number get?