Tagged Questions
2
votes
2answers
131 views
Hard proof concerning the periodicity of trigonometrical functions. Is that a challenge or just trivial
i want to know if exist or if you can develop or give me ideas of a proof to show that the least number for which sine is periodic is $2\pi$
$$\neg \{\exists n\in \mathbb{R} \wedge n < 2\pi: ...
5
votes
3answers
165 views
On Ceva's Theorem?
The famous Ceva's Theorem on a triangle $\Delta \text{ABC}$
$$\frac{AJ}{JB} \cdot \frac{BI}{IC} \cdot \frac{CK}{EK} = 1$$
is usually proven using the property that the area of a triangle of ...
1
vote
0answers
163 views
What is a direct proof of isoperimetric inequality?
What is a direct proof of isoperimetric inequality? In another word, i am asking for a proof that the circle has the maximum area compare to other geometric shape with the same circumstance but ...
3
votes
3answers
155 views
Is there a “simple” proof of the isoperimetric theorem for squares?
"Simple" means that it doesn't use any integral or multivariable calculus concepts.
A friend of mine who's taking a differential calculus course came up with the problem
Prove that among all the ...
1
vote
0answers
89 views
Is this reading of the proposition I.4 of the Elements valid?
I have studied what Heath, Russell, and what others have said about the proposition 4 of the Book I of the Elements. So far, I understand the "problems" they see with using superposition, but I still ...
8
votes
2answers
170 views
What is it that makes this proof about rational rectangles work fundamentally?
I saw this problem several years ago, and I discovered a solution to it. I've since learned a somewhat more efficient solution based on the same idea.
Call a rectangle in the $(x,y)$ plane ...
