Rhapsody on the Proof of Pi = 4 by Vihart
April 5th, 2012 at 6:02 pm 0 notes #proofs #bad math #troll proofs #math #mathematics
Touch Trigonometry!! This sooo awesome!! Major thanks to alexxxanimal for submitting it!
“Touch Trigonometry aims to help math learners of all ages get an intuitive understanding of trigonometry.”
This is just awesome and fun to play around with.
Reblogged from proofmathisbeautiful May 17th, 2011 at 11:42 am 114 notes #mathematics
Reblogged from proofmathisbeautiful August 23rd, 2010 at 3:56 pm 115 notes #futurama #mathematicsA writer for Futurama created a brand new math theorem based on group theory to explain a plot twist in the show. That is like, going way beyond the call of duty, dude.
Ken Keeler, the Futurama writer behind the theorem, actually has a PhD in math, so this was probably just a walk in the park for him. But for the rest of us non math geniuses, his theorem was used to explain a problem with an invention that let characters switch bodies. In the show, you can only switch bodies once with the same pair of people, so they needed an equation to prove that with enough switching bodies around, everyone will eventually end up as who they really are. Insert: funny jokes, robot humor and black comedy and mix accordingly.
Keeler’s theory would mathematically put everybody in the right place so that all could be right in the Futurama world. Without Keeler’s work, Bender’s brain might have ended up in Amy’s body forever! Which, to think about, actually might not be such a bad thing. I’m no Keeler so I can’t explain his theory but you can check out the proof in full here.
(Or…Click Through…)
EDIT: UPDATED INFORMATION ABOUT THIS POST CAN BE FOUND IN THE FOLLOWING LOCATIONS
A very interested look at how math education can be changed.
“Math makes sense of the world. Math is the vocabulary for your own intuition.”
Reblogged from lestranger August 9th, 2010 at 5:22 pm 9 notes #mathematics #education #video #TED
Reblogged from fuckyeahmath February 8th, 2010 at 5:28 pm 133 notes #music #mathematics(via fuckyeahmath)
Funny that you post this. I’m reading Stuart Isacoff’s Temperament that examines how the modern scale was developed and all the hairy math problems it raised, given that musical proportions does not follow perfect proportions as Pythagoras had believed. Excepting for the facts that the book has lenient, if not downright lazy, editors, Isacoff’s writing is syrupy, and his use of parenthetical thoughts rivals that of Joseph Conrad, it’s an interesting topic. Isacoff is a pianist who fails to be the mathematician, physicist, and historian that this book needs, and in some sense, as a musicologist/theorist as well.
Reblogged from proofmathisbeautiful September 16th, 2009 at 6:57 pm 15 notes #mathematics #math #artIn 1882, Felix Klein imagined sewing two Möbius Loops together to create a single sided bottle with no boundary. Its inside is its outside. It contains itself.
Take a rectangle and join one pair of opposite sides — you’ll now have a cylinder. Now join the other pair of sides with a half-twist. That last step isn’t possible in our universe, sad to say. A true Klein Bottle requires 4-dimensions because the surface has to pass through itself without a hole.
It’s closed and non-orientable, so a symbol on its surface can be slid around on it and reappear backwards at the same place.You can’t do this trick on a sphere, doughnut, or pet ferret — they’re orientable.
A true Klein Bottle lives in 4-dimensions. But every tiny patch of the Klein Bottle is 2-dimensional. In this sense, a Klein Bottle is a 2-dimensional manifold which can only exist in 4-dimensions!
Alas, our universe has only 3 spatial dimensions, so even Acme’s dedicated engineers can’t make a true Klein Bottle.
A photograph of a stapler is a 2-dimensional immersion of a 3-dimensional stapler. The true stapler has been flattened into the flatland of the photo. In the same way, our glass Klein Bottles are 3-D immersions of the 4-D Klein Bottle. Acme’s Klein Bottle is a 3-dimensional photograph of a “true” Klein Bottle.
A Klein Bottle cannot be embedded in 3 dimensions, but you can immerse it in 3-D. (An immersion may have self-intersections; Embeddings have no self-intersections. Neither an embedding nor an immersion has folds or cusps.)
We represent a Klein Bottle in glass by stretching the neck of a bottle through its side and joining its end to a hole in the base. Except at the side-connection (the nexus), this properly shows the shape of a 4-D Klein Bottle. And except at the nexus, any small patch follows the laws of 2-dimensional Euclidean geometry.
Contrast this with a corked bottle — say, a wine bottle. It has two sides: inside and outside. You can’t get from one to the other without drilling a hole or popping the top. Once uncorked, it has a lip which separates the inside from the outside. If you make the glass arbitrarily thin, that lip won’t go away. It’ll become more prominent. The lip divides one side of the bottle from the other. So an uncorked bottle is topologically the same as a disc … it has two sides, separated by a boundary — an edge.
But a Klein Bottle does not have an edge. It’s boundary-free, and an ant can walk along the entire surface without ever crossing an edge. This is true of both theoretical Klein Bottles and our glass ones. And so, a Klein Bottle is one-sided
This set of parametric equations defines the surface of every Klein Bottle.:
x = cos(u)*(cos(u/2)*(sqrt_2+cos(v))+(sin(u/2)*sin(v)*cos(v)))
y = sin(u)*(cos(u/2)*(sqrt_2+cos(v))+(sin(u/2)*sin(v)*cos(v)))
z = -1*sin(u/2)*(sqrt_2+cos(v))+cos(u/2)*sin(v)*cos(v)
