17 votes

How can I build a protractor without a protractor?

As Will Orrick says in the comments under user20315's answer, it is possible, with straightedge and compass, to construct a regular 120-gon, and therefore it is possible to mark off every 3 degrees on ...
mweiss's user avatar
  • 17.1k
13 votes

How can I build a protractor without a protractor?

Step 1: Find a machinable material that is reasonably incompressible. Step 2. Find a string material that is reasonably non-stretchy. Step 3: Make a cylinder out of the machinable material (perhaps ...
Jasper's user avatar
  • 3,081
12 votes
Accepted

Geometry in the Community College Curriculum

"Geometry," the American high school course, is generally pseudo-axiomatic Euclidean geometry. I don't know whether your claim about the CC curriculum is broadly true, but assuming it is, it'...
Kevin Arlin's user avatar
7 votes

Geometrical approaches in algebra

I offer this (community wiki) only to illustrate the OP's 2nd example. From the Archimedes Lab Project: Quite beautiful!
6 votes
Accepted

Triples or triplets in Pythagoras theorem

The word “triple” is appropriate here because $(3,4,5)$ is a tuple consisting of three elements. In mathematics, a tuple is a finite ordered list (sequence) of elements... Mathematicians usually ...
Justin Hancock's user avatar
6 votes

Why do standard geometry textbooks not start with trigonometry?

Here is a late but brief answer to the question: If this is the normal way of teaching geometry, why? Why is the course focused more on memorizing theorems rather than understanding where they come ...
Daniel R. Collins's user avatar
6 votes

How can I build a protractor without a protractor?

In mweiss' method, the outer angles ∠AOC and ∠DOB are shy of 1° by slightly more than 0.0001°, and the inner angle ∠COD exceeds 1° by slightly more than 0.0002°. On a (huge!) one meter diameter ...
Jasper's user avatar
  • 3,081
5 votes

Geometry in the Community College Curriculum

The other answers well discuss how geometry is sort of "off track" for the push to calculus and the other topics (trig, algebra) are much more integral. But I don't think they make the ...
meta comment guest's user avatar
4 votes

Geometrical approaches in algebra

This may not be what you have in mind, but your question reminds me of “proofs without words” aka visual proofs. The three examples you gave have relatively famous visual proofs. There’s some ...
Justin Hancock's user avatar
4 votes

How to formalize high-school (Euclidean) geometry?

Clark and Pathania might be of interest to you. "This textbook provides a full and complete axiomatic development of exactly that part of plane Euclidean geometry that forms the standard content ...
BlakeDavis's user avatar
3 votes

Multiple proofs for the same problem

It just crossed my mind that I can offer you some option you haven't probably considered yourself. Once I experimented in my calculus course (which also involved some elements of analytic geometry and ...
fedja's user avatar
  • 3,044
3 votes

Geometry in the Community College Curriculum

Typically, a geometry class in high school teaches Euclidean geometry. Depending on how much time is spent and the exact class, Euclidean geometry as rendered today explores properties of triangle, ...
Argyll's user avatar
  • 131
2 votes

How can I build a protractor without a protractor?

In terms of doing it on paper, it is impossible to trisect (or quintisect) angles with a conventional compass and straight edge. And 180 = 2 * 2 * 3 * 3 * 5. Of course you could be an anti-...
user20315's user avatar
2 votes

Geometrical approaches in algebra

Here's a well-known one: $$\sum_{n=1}^{\infty} \frac{1}{2^n} = 1$$
Dominique's user avatar
  • 1,340
1 vote

Multiple proofs for the same problem

At the college level, see here, here, here, here, and here. Only the first link is suitable for high school courses.
KCd's user avatar
  • 3,008
1 vote

Best demonstration of $\pi$ ever; is this common?

I don't know how common this demonstration is (I never saw it in a class when I was a student), but there's a nice video illustrating it that students can watch: see the first 35 seconds of the ...
KCd's user avatar
  • 3,008

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