Interesting math facts

The Sandbox General
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I’m going to be teaching high school math next year. I’m trying to think of something to put on the board outside the room.

I’d like to come up with some ways that math is used behind the scenes of things the see and use every day.

For example, on a 3blue1brown video he mentioned talking to a Pixar engineer and finding out that to make a movie like Coco about a trillion quadratic equations had to be solved.

Or, if you ask Siri a question, she uses calculus to get the answer.

Complex numbers being used to rotate things in computer animation.

Maybe something about number theory being completely useless for a few hundred years until we needed to encrypt things on the internet.

Any ideas?

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same goes for linear algebra where 3blue1brown has a whole series on it

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In online competitive games, your matchmaking ranking is estimated through statistics and probability

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you can also mention probability is frequently used to solve crime, specifically DNA testing.

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That’s where I got that one too - in his video about quaternions. I didn’t want to go that far…

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I don’t how you would be able to incorporate this onto a board outside the room, but…

Dr Holly Krieger did a Numberphile video back in 2015 where she showed how you can find Pi within the Mandelbrot Set. It kind of blew my mind. I found it to be an interesting math fact for sure.

Pi and the Mandelbrot Set - Numberphile

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You could show a graph of mortality rates by age and sex and point out the bump for ~16-~20 yo’s..especially males. That’s always a fun topic to bring up at parties.

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“Why does a life insurance policy paying $10,000 cost $x for a 16-year old applicant?”
(Where x = a quote from some insurance company.)

“How is the elevation of Mt Everest (or a local mountain) determined?”

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Why males car insurance is higher during those years than females?

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Good for you!

I don’t have any glittery stuff to suggest. However when I first saw that “e” raised to the power of (i*pi) was equal to -1 it blew my mind how all of these elements came together in one formula. Senior math students might appreciate this.

When I went to university I noticed the formula was even inscribed in large lettering over the entrance to the main women’s residence.

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do HS students know what e is? I don’t remember

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:ditto:

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A good explanation for why this is, using the infinite power series for e^x and de Moivre’s formula, neither of which are taught until at calc, possibly not until Calc II (AP Calc BC?):
math.toronto.edu/mathnet/questionCorner/epii.html

For non-milk milk guy, it might be something to put on the board the week you discuss such things.
It’s not everyday stuff, though.

Surveying in olde times.

Surveyors work with elements of geodesy, geometry, trigonometry, regression analysis, physics, engineering, metrology, programming languages, and the law. They use equipment, such as total stations, robotic total stations, theodolites, GNSS receivers, retroreflectors, 3D scanners, LiDAR sensors, radios, inclinometer, handheld tablets, optical and digital levels, subsurface locators, drones, GIS, and surveying software.

Also:
Mapping out and painting the lines of a soccer field from scratch, using geometry of straight edge and compasses. (Need to make perpendicular lines and circles.)

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Don’t they take that stuff at raves???

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I think my son used it this year in algebra II, which is what I’ll be teaching. (Maybe a few geometry classes, it’s still up in the air)

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I saw a reel recently of a carpenter who used whole number right triangles to make sure what ever it was he was making was square. Pythagoras’ Formula.

And, of course, trig functions for all kinds of things that they do that they simply don’t realize it is based on math.

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Telephone and electrical wires always hang in a catenary curve.

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Show how to use two drafting triangles to draw parallel lines.

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no idea what Algebra 2 is about.

But one thing that astounded me was how you can use algebra to solve for expectations that are seemingly cumbersome

Game: flip a coin, head you win, tail you flip again. What’s the expected number of flips until you win.

Solution: E(x) = 0.5*(1) + 0.5*(E(x)+1) solve for E(x)

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This is an excellent suggestion. You can also show them at some time the formula corresponding to the shape of the curve to make the formula come alive.