Showing posts with label Euler-crazy. Show all posts
Showing posts with label Euler-crazy. Show all posts

5/19/14

e


is a mathematical constant. A mathematical constant is any well-defined real number that is significantly interesting in some way. e has a value of about 2.718. e is an irrational number. It is named after Leonhard Euler and can also be called Euler's number because Euler proved e is an irrational number.
You can calculate e with this formula: 1 + 1/1! +1/2! +1/3! +1/4! +1/5! + 1/6! + 1/7! and so on so forth. if calculated out, the first few terms are 1 + 1 + 1/2 + 1/6 + 1/24 + 1/120 = 2.718055556. 
e is found in many interesting areas. To memorize e, remember this sentence:
to express e remember to memorize a sentence to simplify this.
(count the letters).
The value of e is used to find a nonlinear increase or decrease. e occurs naturally with some frequency so it is the base of natural logarithms.


 &  
next time: logarithms



5/18/14

More Euler, Less History!

Ok, well first of all, Euler is awesome.However I couldn't really find history on his really cool formula, so I figured I'd just blog normally. Anyways, I thought I'd blog about Euler's formula. Euler's formula, first of all is V-E+F=2  or V+F-E=2. V for vertices, E for edges and F for faces. Basically, this means the number of vertices and faces of a convex polyhedron(Click here for a definition!) will always be 2 more than the number of edges of the same polyhedron. Try it out! If a convex polyhedron(in this case a cube) has 8 vertices, 6 faces and 12 edges, what does the formula look like? That would be 8+6-12=2. You may find that some numbers don't work, but that's probably because your solid is just not a convex polyhedron. However, V+F-E can also equal 1and/or other values, so Euler's characteristic was made. He's pretty smart, huh? Anyway, the general formula is V+F-E=x.That is where Euler's characteristic comes in. Umm... so this is an ultra short blog, read up and  things I already explained here! Because Math is Fun! ;D See Ya!

Look it's Euler!!