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I've been taking Geometry and the year is ending. I have come to realize that it is centered around the Pythagorean theorem. Is it unique in this feature or will many classes be centered around this in the future? If so, what?

Edit: when I say 'centered' I really mean fundamentally connected to and 1-2 easy 'thought' steps away.

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  • $\begingroup$ Geometry is very interesting you gonna see topics like triangles,circle, Euler line, cyclic cuadrilater, circumference of the 9points, papus theorem, power of a cyrcle, and more topics. $\endgroup$
    – user795628
    May 11, 2021 at 23:01
  • $\begingroup$ The Pythagorean theorem is useful when determining the distance between 2 points. So at any point when you want to find something that involves distance (speed, position, acceleration, height that a ladder can safely reach, etc), you'll most likely use it. $\endgroup$
    – Ryan
    May 11, 2021 at 23:01
  • $\begingroup$ It is the primary method of determining distance in Euclidean spaces, but that is an undertone, rather than any day-to-day thing. But almost any place using geometry, it is there somewhere. You’ll rarely have to refer to the theorem directly, though. $\endgroup$ May 11, 2021 at 23:03
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    $\begingroup$ But trigonometry is all about right triangles, so you get a lot of it there. $\endgroup$ May 11, 2021 at 23:07
  • $\begingroup$ One of the weird places where it comes up is in statistics. In statistics, there is no reason to think the distance between two datasets is naturally Euclidean. You might think to calculate the errors in an estimate in a few ways, but the “standard deviation” is the calculated as the (scaled) square root of the sum of squares. This might be preferred because Pythagorean distances tend to be easier to use, rather than any “natural” version. Not only does Pythagorus have geometric properties, but it has algebraic properties. $\endgroup$ May 11, 2021 at 23:29

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The people in the best position to answer your question are the math teachers at your school, so I'd encourage you to ask (one or more of) them.

Having said that, I don't think you'll see old Pythagoras much when you come to algebra and solving equations and solving systems of equation. He'll put in more of an appearance when you get to analytic geometry and Calculus, but that theorem won't be the be-all and end-all of those subjects.

And if you make it all the way to Category Theory, you can probably wave Pythagoras goodbye.

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