Mathematician, mathematics educator and mathematics enthusiast. Also at @normalsubgroup@mathstodon.xyz. He/Him
Jun 23, 2020 • 68 tweets • 24 min read
1/n. Slow-moving thread on a series of related, relaxing puzzles. They all involve this game:
Label all vertices and edges of a graph. Use each number 1,2,3,... exactly once (don’t miss any). At each vertex the sum of its label and its incident edge labels must be a constant, h. 2/n The labeling is called “total” because vertices AND edges are labeled.
It’s called “vertex magic” because we form a sum at each vertex, and—magically—get the same result (called the magic constant) each time.
The 2 examples suggest questions, eg: which constants are ok&why?
Feb 15, 2020 • 14 tweets • 4 min read
(1/11) I've seen this posted a lot, but usually not with many comments. This thread has:
1. A version for teachers (ready to go for the class)
More importantly:
2. A view that promotes a richer, more human view towards algebra. nytimes.com/2020/02/05/sci…
(2/11) As a disclaimer, I didn't read the article carefully. I do what I normally do, look just enough until I see an idea, and then go and recreate a version. This is how I (and probably most) mathematicians operate.
Therefore, this may look nothing like what's in the article.
Feb 9, 2020 • 14 tweets • 5 min read
The 1/7 (of area) triangle theorem.
How knowing *about* Linear Algebra makes this an exciting and doable exercise.
A problem exploration thread (1/14).
(2/14) The Problem:
Take triangle ABC. Let A’ be the point in BC that’s twice as far from C as from B.
Similarly, B’ ... on CA twice as far from A as C
C’....on AB 2ce as far from B as A
Connect AA’, BB’, CC’. Prove the middle triangle has 1/7 the area of the original, ABC.
Feb 8, 2020 • 15 tweets • 5 min read
The 1/7 (of area) triangle theorem.
How knowing *about* Linear Algebra makes this an exciting and doable exercise.
A problem exploration thread (1/14).
(2/14) The Problem:
Take triangle ABC. Let A’ be the point in BC that’s twice as far from C as from B.
Similarly, B’ ... on CA twice as far from A as C
C’....on AB 2ce as far from B as A
Connect AA’, BB’, CC’. Prove the middle triangle has 1/7 the area of the original, ABC.
Sep 7, 2019 • 9 tweets • 3 min read
1/n I believe very strongly in learning guessing. But how do we teach this in the classroom?
Here’s a small example, which happened as part of a precalculus review for calc I students a couple of weeks ago:
2/n The first class, I solicited guesses for the answer to the following:
find two numbers whose sum is 5 and whose product is a maximum. 2 and 3 was suggested, followed by the question: do they have to be integers?
This led to a guess of 2.5 and 2.5.
