number theory
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…
Testing Patterns
Hello mathematicians, puzzlers, and other curious people! This video contains three conjectures, one proof, and one counterexample (and therefore one open conjecture), based on this previous post. The important idea of what we did here is if we can find a formula that\’s equivalent to how we\’re coming up with some numbers, and that formula…
Square Numbers
Hello mathematicians, puzzlers, and other curious people! For those who don\’t already know, when you take a number and multiply it by itself, the product is called a square number because we can use it to draw a square neatly, such as these numbers: Sometimes you will hear people refer to numbers as \”___ squared,\”…