Math for a cake - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-22T11:22:11Z http://mathoverflow.net/feeds/question/117494 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/117494/math-for-a-cake Math for a cake Frank 2012-12-29T09:55:13Z 2012-12-29T22:15:47Z <p>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.</p> <p>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". </p> <p>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.)</p> <p>Any ideas what we could put on top of the cake?</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117495#117495 Answer by Yuichiro Fujiwara for Math for a cake Yuichiro Fujiwara 2012-12-29T10:00:54Z 2012-12-29T10:00:54Z <p>$e^{i \pi} = -1$</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117496#117496 Answer by Julian Kuelshammer for Math for a cake Julian Kuelshammer 2012-12-29T10:09:38Z 2012-12-29T10:09:38Z <p>$\mathrm{P}=\mathrm{NP}$ or $\mathrm{P}\neq \mathrm{NP}$, whichever you prefer.</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117498#117498 Answer by Qfwfq for Math for a cake Qfwfq 2012-12-29T10:18:59Z 2012-12-29T16:38:14Z <p>Euler's classical formula for convex polyhedra</p> <p>$$v-e+f=2$$</p> <p>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.</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117500#117500 Answer by Qfwfq for Math for a cake Qfwfq 2012-12-29T10:38:11Z 2012-12-29T10:38:11Z <p>My all-time favourite formula: Stokes theorem</p> <p>$$\int_{M}\mathrm{d}\omega=\int_{\partial M}\omega$$</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117501#117501 Answer by Dmitri Pavlov for Math for a cake Dmitri Pavlov 2012-12-29T10:40:24Z 2012-12-29T10:40:24Z <p>How about the Grothendieck-Hirzebruch-Riemann-Roch formula: ch(f<sub>!</sub>F) = f<sub>*</sub>(ch(F)td(T<sub>f</sub>))?</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117510#117510 Answer by Lee Mosher for Math for a cake Lee Mosher 2012-12-29T13:52:28Z 2012-12-29T13:52:28Z <p>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.</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117511#117511 Answer by Gottfried Helms for Math for a cake Gottfried Helms 2012-12-29T13:59:42Z 2012-12-29T14:13:11Z <p>One which I like much is $$\exp \left(\begin{bmatrix} . &amp; . &amp; . &amp; . &amp; .\\ 1 &amp; . &amp; . &amp; . &amp; . \\ . &amp; 2 &amp; . &amp; . &amp; . \\ . &amp; . &amp; 3 &amp; . &amp; . \\ . &amp; . &amp; . &amp; 4 &amp; . \\ \end{bmatrix} \right)= \begin{bmatrix} 1 &amp; . &amp; . &amp; . &amp; . \\ 1 &amp; 1 &amp; . &amp; . &amp; . \\ 1 &amp; 2 &amp; 1 &amp; . &amp; . \\ 1 &amp; 3 &amp; 3 &amp; 1 &amp; . \\ 1 &amp; 4 &amp; 6 &amp; 4 &amp; 1 \\ \end{bmatrix}$$ 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: $$\Large \exp \small \left(\begin{bmatrix} . &amp; . &amp; . &amp; . \\ 1 &amp; . &amp; . &amp; . \\ . &amp; 2 &amp; . &amp; . \\ . &amp; . &amp; 3 &amp; . \\ \end{bmatrix} \right)= \begin{bmatrix} 1 &amp; . &amp; . &amp; . \\ 1 &amp; 1 &amp; . &amp; . \\ 1 &amp; 2 &amp; 1 &amp; . \\ 1 &amp; 3 &amp; 3 &amp; 1 \\ \end{bmatrix}$$</p> <p>With a bit explanation which might be useful for other guests <a href="http://go.helms-net.de/math/binomial/index-Dateien/image008.png" rel="nofollow">http://go.helms-net.de/math/binomial/index-Dateien/image008.png</a> </p> http://mathoverflow.net/questions/117494/math-for-a-cake/117512#117512 Answer by Gottfried Helms for Math for a cake Gottfried Helms 2012-12-29T14:05:26Z 2012-12-29T14:05:26Z <p>A geometric one, where the zero can be made a cake (circle) itself $$x^2 + y^2 -1 = \Huge \circ$$</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117514#117514 Answer by Steven Landsburg for Math for a cake Steven Landsburg 2012-12-29T14:13:14Z 2012-12-29T14:13:14Z <p>196884 = 196883 + 1</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117518#117518 Answer by Barry Cipra for Math for a cake Barry Cipra 2012-12-29T14:35:04Z 2012-12-29T14:35:04Z <p>Not famous, perhaps, but how about</p> <p>$$\int_0^a f_A(x)dx = \int_a^1 f_A(x)dx = 1/2$$</p> <p>from <a href="http://www.ams.org/notices/200611/fea-brams.pdf" rel="nofollow">Better Ways to Cut a Cake</a> by Brams, Jones, and Klamler?</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117520#117520 Answer by Simon Lyons for Math for a cake Simon Lyons 2012-12-29T14:49:27Z 2012-12-29T14:49:27Z <p>22/7. Because a cake is, approximately, a pi(e).</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117525#117525 Answer by anony for Math for a cake anony 2012-12-29T15:18:07Z 2012-12-29T15:18:07Z <p>(comment to D. Pavlov) I once attempted to bake GRR onto cookies (leavened with <a href="http://en.wikipedia.org/wiki/Hartshorn" rel="nofollow">hartshorn</a>, naturally). It didn't turn out too legible, but probably doable with icing.</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117537#117537 Answer by Paul Siegel for Math for a cake Paul Siegel 2012-12-29T17:03:04Z 2012-12-29T17:03:04Z <p>At Michael Atiyah's 80th birthday conference, the cake had the Atiyah-Singer index formula:</p> <p>$$\text{Ind}(D) = \int_{T^*M} \text{ch}(\sigma_D) \text{Todd}(TM \otimes \mathbb{C})$$</p> <p>I can verify that it made the cake even more delicious.</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117548#117548 Answer by Goldstern for Math for a cake Goldstern 2012-12-29T18:39:27Z 2012-12-29T18:39:27Z <p>Gödel's completeness theorem: A (first order) sentence $\varphi$ is provable from the axioms $\Sigma$ iff it holds in every model of $\Sigma$: $$\Sigma \vdash \varphi \Leftrightarrow \Sigma \vDash \varphi$$</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117551#117551 Answer by Goldstern for Math for a cake Goldstern 2012-12-29T18:46:36Z 2012-12-29T18:46:36Z <p>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): $$\Box \lnot \Box \bot \Rightarrow \Box \bot.$$</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117555#117555 Answer by Gerhard Paseman for Math for a cake Gerhard Paseman 2012-12-29T19:45:28Z 2012-12-29T19:45:28Z <p>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.</p> <p>(There is also an interactive n player version.)</p> <p>Gerhard "Save A Piece For Me" Paseman, 2012.12.29</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117557#117557 Answer by Asaf Karagila for Math for a cake Asaf Karagila 2012-12-29T20:05:59Z 2012-12-29T20:05:59Z <p>While it's <a href="http://boolesrings.org/asafk/2012/math-cookies/" rel="nofollow">math for a cookie</a>, I'm sure it can be done on a cake as well. </p> <p>$$|X|\lt|\mathcal P(X)|$$</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117559#117559 Answer by Gerald Edgar for Math for a cake Gerald Edgar 2012-12-29T20:22:09Z 2012-12-29T20:22:09Z <p>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.</p> http://mathoverflow.net/questions/117494/math-for-a-cake/117566#117566 Answer by Glen M Wilson for Math for a cake Glen M Wilson 2012-12-29T22:15:47Z 2012-12-29T22:15:47Z <p>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: <a href="http://tex.stackexchange.com/questions/3892/how-do-you-draw-the-snake-arrow-for-the-connecting-homomorphism-in-the-snake-l" rel="nofollow">http://tex.stackexchange.com/questions/3892/how-do-you-draw-the-snake-arrow-for-the-connecting-homomorphism-in-the-snake-l</a></p>