proof

  • Identity Crisis? Identity Resolution?

    Hello mathematicians, puzzlers, and other curious people! Whilst doing homework for my numerical methods class (which is about getting computers to do math for you), and using GeoGebra to troubleshoot a result that wasn’t working out, I ran into an issue: GeoGebra’s expression for a derivative was different from what I had calculated by hand.…

  • Comparing Infinities

  • A \”Power\”ful Conjecture

    Hello mathematicians, puzzlers, and other curious people! A conjecture came up in a homeschool group the other day. The student had been doing the kind of thing we believe in around here, looking for patterns in numbers, and noticed that the first several \”even powers of 2\” — by which they meant 2 raised to…

  • Beginning of Pythagorean Intro to Number Theory Study-Along

    Hello mathematicians, puzzlers, and other curious people! Don\’t forget, this is the first week of our Pythagorean Intro to Number Theory Study-Along! You can still sign up for the free class and get started today on taking a proof-based look at numbers and geometry. Calc You Later!

  • Free books and classes!

    Hello mathematicians, puzzlers, and other curious people! You may have already perused Springer\’s free ebook offerings (see the link to them in the distance learning section of the referral page if you haven\’t) — if not, make sure you do, because some of them are not to be missed and the free download opportunity won\’t…

  • Multiplying Square Numbers

    Hello mathematicians, puzzlers, and other curious people! Following up this previous post on square numbers, in this video I take a look at what happens when two square numbers are multiplied. As you can see, when you think you\’ve found a number pattern, formulas can help with showing whether that pattern will always work or…

  • The Abstract Algebra of Direct Proportions

    Hello mathematicians, puzzlers, and other curious people! This post previously appeared in the Mathematical Musings free class on Teachable, currently available in the Teachable archive. In a previous MMusing, I mentioned a rabbit trail upon the occasion of using the word \”group\” about functions in the form f(x)=kx, called direct proportions. I didn\’t run down…