The little boy and I were talking about math at school this morning, and today’s topic was geometry. I’m glad to know that he already has a reasonable understanding of the Pythagorean Theorem: I was telling him that I was about the same age he was when I first came across it, but in my case I had a practical rather than a theoretical motivation for learning it.
It was the 1980s, and I was teaching myself. Dr LogoDigital Research’s implementation of the Logo programming language (possibly from this book). One day, I was writing a program to create an indoor scene, which included a window through which a mountain was visible. My aim was to produce something like this:
All of these graphics were created using my own implementation of the 2019 logo, TRRTL.COM: Click on any graphic to continue drawing!
my window was 300 “steps”
When I came to make my first attempt at the mountain it was 200 steps wide and bifurcated in both directions.
And so, naively, starting from the bottom-left, I thought I would need some code like this:
RIGHT 45 FORWARD 100 RIGHT 90 FORWARD 100
But what I finally got was this:
Ear? More like need-another-try-potnews.
I immediately realized my mistake: Absolutely The sides of the mountain will need to be lengthened so that the peak reaches the mid-point of the window and the far side hits its far corner. But How much This should happen more now.
I realized that the numbers I’m looking for must be greater than 100 but less than 250: logically, these were Limit I was working inside. 100 would be perfect if my line was horizontal (a “flat” mountain?), and 250 would be long enough to go the “long way” to the center point of the window (100 along, and 150 on top). So I guessed 150 and… it was close enough… but still wrong:
I remember being confused and disappointed that the result was so close but still wrong. Of course, this is because the relationship between the side lengths of a triangle is not in a 1:1 manner, but this was the first time I had to think about this. Why,
So I found my mom and asked her what I was doing wrong. I’m sure he would have been delighted to dust off the rarely-accessed knowledge of his school years and teach me about Pythagoras!
Undoubtedly, the correct answer is given by:
I use MathML so rarely that I have to look at the syntax.
Therefore, the answer is… 141.421 (up to three decimal places). So I rounded up to 141 and my diagram worked!
What made this math lesson from my mother so memorable was that It provided a concrete goali had something i wanted to receiveAnd I learned the math I needed to get there. And now it is indelibly imprinted on my mind.
I learned to do quadratic equation formulas and algebraic integration by rote, and I guarantee it is less well established in my long-term memory than the sine and cosine rules or solving simultaneous equations because I need to do this often They Things outside the classroom!
So I guess the lesson is that I should try to keep an eye on practical applications of math that I can share with my children. Real problems that are interesting to solve, to help create a memorable grounding that supports the more challenging and abstract abstract mathematics they may wish to pursue later.
Both children are sharp young mathematicians, and the younger one particularly enjoys it, so it seemed worthwhile to feed that passion. Maybe I should show them TRRTL.COM so they can try their hand at the logo!
<a href