/sci/ - Science & Math

>>4909210

While I agree with your statements, I disagree with Euclid being the most influential to geometry for the same reasons. Most things about geometry were already known for thousands of years before Euclid. What Euclid did do however that was pretty astonishing was Axiomatize it all down to a handful of axioms. This did a lot for axiomatization of mathematics as a whole, but very little for mathematics in my opinion. On a sidenote, one of the things that euclid was concerned with was compass and straightedge constructions, something that a lot of people know very little about [but in my opinion is very interesting] and was actually really incomplete until the 1800s when proofs were provided to show what numbers can and can't be constructed (and in the process create proofs such as 'it is impossible to construct a heptagon with a compass and straightedge'). I would argue that a person learns more about geometry through art or autocad classes than they do from geometry classes, because all they seem to focus on is axiomatization.

>>4909279

Some things, but how important they are depends on what you think is important to mathematics.

So I am stuck at a problem: n2^n < 3^n

Proving with full induction.
P(n) ::= n2^n < 3^n
P(n+1) =
(n+1)2^(n+1) = 2*n * 2^n + 2*2^n < 2*3^n + 2*2^n

I am stuck at this step, does anyone know how to continue?