Question (1 Viewer)

[abdooooo!!!]

how do you know a triangle has 180 degrees and what is a prime number?

 

[Grey Council]

prime number = a number having whole number factors of itself and one ONLY.

180 degrees, its from how we define a circle, and i suppose the 180 degrees in a triangle comes from drawing a triangle within a circle or some such. :-\ don't know the exact prrof

 

[abdooooo!!!]

umm what is the use of prime numbers? is there any use at all?

edit: and why are you up so early?

 

[Grey Council]

prolly same as you:
prayer.

prime numbers are used to create high security codes and god knows what else. main use is in cryptology, i think.

 

[fitz33]

Originally posted by abdooooo!!!
how do you know a triangle has 180 degrees

triangles only have 180 degrees in euclidean geometry, where this fact can be derived from the axioms. however, one of the axioms (the last one, about parallel lines) is kinda controversial, and this axiom has to be used to prove a triangle has 180 degrees. therefore, mathematicians also 'invented' non-euclidean geometry, in which the sum of the angles in a triangle is not equal to 180 degrees.

and before you ask, non-euclidean geometry does actually have practical uses in physics. (lots of important things rely on it).

 

[turtle_2468]

eg spherical geometry...
On a unit sphere, the angle being "what you'd expect", the sum of the angles minus 2Pi (in radians) equals the area of said triangle.

 

[freaking_out]

Originally posted by fitz33
triangles only have 180 degrees in euclidean geometry, where this fact can be derived from the axioms. however, one of the axioms (the last one, about parallel lines) is kinda controversial, and this axiom has to be used to prove a triangle has 180 degrees. therefore, mathematicians also 'invented' non-euclidean geometry, in which the sum of the angles in a triangle is not equal to 180 degrees.

and before you ask, non-euclidean geometry does actually have practical uses in physics. (lots of important things rely on it).

yeah, i heard that triangles on different surfaces (such as curved ones) don't have angles adding up to 180 degrees.

 

[Euler]

prime numbers are fascinating. There are 25 from 0 to 100,
21 from 100 to 200,
16 from 200 to 300,
16 from 300 to 400,
17 from 400 to 500,
...

There's no obvious pattern.

prime numbers are the building blocks of all positive integers, one application mentioned was cryptography.

There are infinitely many primes. There are two types of odd primes: 4k+1 and 4k+3. There are infinitely many of each type.

For an arithemetic sequence an+b, where a and b have no common factors, the sequence contains infinitely many primes. This was proved by Dirichlet.

There is no exact formula which calculates what the nth prime is.

To know the exact distribution of the primes [i.e. pi(x)=number of primes less than x] is closely related to Riemann's Hypothesis.

The twin prime conjecture: there are infinitely many primes with a difference of 2; eg. 11 and 13, 17 and 19, 41 and 43.

I'm sure there are many more reasons why primes are interesting.

 

[Euler]

In Euclidean (regular) geometry, one way to prove that the sum of the angles is two right angles is to consider one of the exterior angles and add, from that vertex, a parallel line to the opposite side. Chase some angles around and you would have divided the 'straight line angle' into three parts, all of which equal the different angles of the triangle.

 

[abdooooo!!!]

umm... interesting... thanks people.