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 ...
- 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 ...
- 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'...
- 641
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 ...
- 1,829
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 ...
- 22.8k
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 ...
- 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 ...
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 ...
- 1,829
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 ...
- 101
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 ...
- 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, ...
- 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-...
- 37
2
votes
Geometrical approaches in algebra
Here's a well-known one:
$$\sum_{n=1}^{\infty} \frac{1}{2^n} = 1$$
- 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.
- 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 ...
- 3,008
Only top scored, non community-wiki answers of a minimum length are eligible