2
votes
1answer
103 views

Do circles exist

So I was wondering about circles today and if they really do exsist. If you graph a circle in function mode, your equation looks like$$y=\sqrt{1-x^2}$$ Now for simple purposes lets take a portion of ...
0
votes
3answers
113 views

Is there any geometry where ratio of circle's circumference to its diameter is rational?

In Euclidean geometry, the ratio of the circumference of a circle to its diameter is an irrational number, 3.14159 and so on. But if you change to non-Euclidean geometries, you get other values for ...
0
votes
1answer
197 views

Spiral of Theodorus - Discussion

The fact that $\sqrt2$ is not rational goes back to Theodorus of Cyrene from the school of Pythagoras, and is discussed in Plato's dialog "Theaetetus". Of course, $\sqrt n$ is not rational for any ...
15
votes
2answers
377 views

Do there exist an infinite number of 'rational' points in the equilateral triangle $ABC$?

Let's call a point $P$ which satisfies the following condition 'a rational point'. Condition: Each distance $PA, PB, PC$ from a point $P$ to three vertices $A, B, C$ of an equilateral triangle $ABC$ ...
4
votes
3answers
129 views

prove that $\sqrt{2}$ is irrational using only geometry

Prove that $\sqrt{2}$ is irrational using only geometric concepts and proofs. The proof should look like a proof in Euclid's elements or standard high school geometry. No algebra is allowed. (I know ...
-1
votes
2answers
1k views

Are “perfect” circles mathematically impossible (and do irrational numbers exist)? [closed]

It occurred to me that while $\pi$ is an irrational number, it is nevertheless the ratio between the circumference and diameter of all circles. This seems like a contradiction. Thinking about it ...
11
votes
1answer
230 views

A hole puncher that hates irrational distances [duplicate]

Possible Duplicate: Irrational painting device I have a special hole puncher that does the following: When applied to any point $ x \in \mathbb{R}^{2} $, it removes all points in $ ...
3
votes
2answers
88 views

How do continuity, distance and irrationals arise from discreteness?

Consider a square as rendered on a computer screen: its width and height are $N$ pixels each, and its area is $N^2$ pixels. Its diagonal, when measured in pixels, is also $N$ pixels long. If you ...
1
vote
1answer
159 views

Does anybody know the formula for a quasicrystal structure?

I am an architecture student researching into quasicrystals with the hope of applying it to form a complex truss system. I was wondering if anyone new of a formula for the structure? thanks in ...