Math for a cake - MathOverflow [closed]

Math for a cake

2012-12-29T09:55:13Z

My wife likes to decorate birthday cakes. She told me that she will make a math cake for my birthday and I should provide her a "famous math formula" to be written on the top of the cake.

I realized I can name dozens of physics related famous formulas that one could recognize (Maxwell's equations, Newtons laws, Einstein's $E=mc^2$...) but I couldn't name one that would be more "math related".

Writing some axioms wouldn't work, they take too much space. The famous theorems I know of are not really "a formula" but more like of "statements" that would need some background, or they are not visually appealing (like Fermat's last theorem). (Quests are not math-oriented thus the visual side matters.)

Any ideas what we could put on top of the cake?

Answer by Yuichiro Fujiwara for Math for a cake

2012-12-29T10:00:54Z

$e^{i \pi} = -1$

Answer by Julian Kuelshammer for Math for a cake

2012-12-29T10:09:38Z

$\mathrm{P}=\mathrm{NP}$ or $\mathrm{P}\neq \mathrm{NP}$, whichever you prefer.

Answer by Qfwfq for Math for a cake

2012-12-29T10:18:59Z

Euler's classical formula for convex polyhedra

$$v-e+f=2$$

where $v$ is the number of vertices, $e$ the number of edges and $f$ the number of faces of a convex triagulated polyhedron in $3$-space.

Answer by Qfwfq for Math for a cake

2012-12-29T10:38:11Z

My all-time favourite formula: Stokes theorem

$$\int_{M}\mathrm{d}\omega=\int_{\partial M}\omega$$

Answer by Dmitri Pavlov for Math for a cake

2012-12-29T10:40:24Z

How about the Grothendieck-Hirzebruch-Riemann-Roch formula: ch(f_!F) = f_*(ch(F)td(T_f))?

Answer by Lee Mosher for Math for a cake

2012-12-29T13:52:28Z

In a different vein from the other answers, how about one of the classic visualizations of the proof of the Pythagorean theorem? It's basically just a bunch of triangles and squares rearranged in a couple ways, and would come out nicely with cake decorator colors. And folks might actually recognize it.

Answer by Gottfried Helms for Math for a cake

2012-12-29T13:59:42Z

One which I like much is $$ \exp \left(\begin{bmatrix} . & . & . & . & .\\ 1 & . & . & . & . \\ . & 2 & . & . & . \\ . & . & 3 & . & . \\ . & . & . & 4 & . \\ \end{bmatrix} \right)= \begin{bmatrix} 1 & . & . & . & . \\ 1 & 1 & . & . & . \\ 1 & 2 & 1 & . & . \\ 1 & 3 & 3 & 1 & . \\ 1 & 4 & 6 & 4 & 1 \\ \end{bmatrix}$$ It is practically easier and a bit more iconic if we reduce it a bit - although for me it is not so pleasing, because the immediate remembering of the Pascal-triangle comes with the 1-4-6-4-1-row: $$ \Large \exp \small \left(\begin{bmatrix} . & . & . & . \\ 1 & . & . & . \\ . & 2 & . & . \\ . & . & 3 & . \\ \end{bmatrix} \right)= \begin{bmatrix} 1 & . & . & . \\ 1 & 1 & . & . \\ 1 & 2 & 1 & . \\ 1 & 3 & 3 & 1 \\ \end{bmatrix}$$

With a bit explanation which might be useful for other guests http://go.helms-net.de/math/binomial/index-Dateien/image008.png

Answer by Gottfried Helms for Math for a cake

2012-12-29T14:05:26Z

A geometric one, where the zero can be made a cake (circle) itself $$ x^2 + y^2 -1 = \Huge \circ $$

Answer by Steven Landsburg for Math for a cake

2012-12-29T14:13:14Z

196884 = 196883 + 1

Answer by Barry Cipra for Math for a cake

2012-12-29T14:35:04Z

Not famous, perhaps, but how about

$$\int_0^a f_A(x)dx = \int_a^1 f_A(x)dx = 1/2$$

from Better Ways to Cut a Cake by Brams, Jones, and Klamler?

Answer by Simon Lyons for Math for a cake

2012-12-29T14:49:27Z

22/7. Because a cake is, approximately, a pi(e).

Answer by anony for Math for a cake

2012-12-29T15:18:07Z

(comment to D. Pavlov) I once attempted to bake GRR onto cookies (leavened with hartshorn, naturally). It didn't turn out too legible, but probably doable with icing.

Answer by Paul Siegel for Math for a cake

2012-12-29T17:03:04Z

At Michael Atiyah's 80th birthday conference, the cake had the Atiyah-Singer index formula:

$$\text{Ind}(D) = \int_{T^*M} \text{ch}(\sigma_D) \text{Todd}(TM \otimes \mathbb{C})$$

I can verify that it made the cake even more delicious.

Answer by Goldstern for Math for a cake

2012-12-29T18:39:27Z

Gödel's completeness theorem: A (first order) sentence $\varphi$ is provable from the axioms $\Sigma$ iff it holds in every model of $\Sigma$: $$ \Sigma \vdash \varphi \Leftrightarrow \Sigma \vDash \varphi$$

Answer by Goldstern for Math for a cake

2012-12-29T18:46:36Z

Gödels incompleteness theorem in the language of modal logic (where $\Box\varphi$ means that $\varphi$ is provable - say in Peano Arithmetic - and $\bot=\lnot \top$ is any false statement): $$\Box \lnot \Box \bot \Rightarrow \Box \bot.$$

Answer by Gerhard Paseman for Math for a cake

2012-12-29T19:45:28Z

I think the diagram should be several dotted rays emanating from the same point, arranged so that if you cut along the lines, each piece will have the same volume of cake and of frosting. It is an impressive diagram when the number of pieces is a not too small odd number such as 5, 7, or 9.

(There is also an interactive n player version.)

Gerhard "Save A Piece For Me" Paseman, 2012.12.29

Answer by Asaf Karagila for Math for a cake

2012-12-29T20:05:59Z

While it's math for a cookie, I'm sure it can be done on a cake as well.

$$|X|\lt|\mathcal P(X)|$$

Answer by Gerald Edgar for Math for a cake

2012-12-29T20:22:09Z

Maybe just make the cake in the shape of a golden rectangle, and use two colors of icing to show the decomposition into a square and a smaller golden rectangle.

Answer by Glen M Wilson for Math for a cake

2012-12-29T22:15:47Z

How about the snake lemma? It's not a formula, but it could still look great on a cake! Plenty of excellent .tex diagrams here: http://tex.stackexchange.com/questions/3892/how-do-you-draw-the-snake-arrow-for-the-connecting-homomorphism-in-the-snake-l