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I'm a pure math dude at heart, even if I don't get to do it much any more. Two years ago, my wife asked me, "If you had to get a math equation tattooed on your
by pflats 7y ago
I'm a pure math dude at heart, even if I don't get to do it much any more.
Two years ago, my wife asked me, "If you had to get a math equation tattooed on your body, what would it be?" I answered, "i^2 = j^2 = k^2 = ijk = -1".
I felt a brief flush of anger when I saw this headline.
This is an extraordinarily good article that should be read by pretty much anyone doing graphics programming.
- s_dev 7y agohttps://en.wikipedia.org/wiki/Broom_Bridge https://en.wikipedia.org/wiki/Broom_Bridge You're like this Irish bridge that has the notation inscribed on it as well. I would like to own an OpenGL kettle with the expression on it.
- andybak 7y ago> I would like to own an OpenGL kettle Do you mean the Utah Teapot?
- s_dev 7y agoYes -- I don't even know why I had the word kettle in my head.
- war1025 7y agoI knew what you meant and didn't even consider that it was the wrong name, for what it's worth. Kettle and teapot are synonyms as far as I'm concerned.
- jfengel 7y agoKettles go on the stove (or have a built in heater), and are used for boiling water. You pour the boiling water into a teapot, usually made of ceramic, which holds the tea leaves. Not that it's important, but now ya know.
- bmn__ 7y agoThese are different equipment. A kettle is used for heating water. In earlier times, it was made out of metal and put onto a heat source (fire, stovetop). Nowadays it is almost entirely displaced by the electric kettle, which is commonly made out of plastic and contains a metal heating plate or spiral on the inside. A teapot is a ceramic pitcher where you put the boiling water and tea leaves to brew the tea.
- DonHopkins 7y agoThey're both called black. https://en.wiktionary.org/wiki/pot,_meet_kettle https://en.wiktionary.org/wiki/pot,_meet_kettle https://en.wiktionary.org/wiki/pot_calling_the_kettle_black#English https://en.wiktionary.org/wiki/pot_calling_the_kettle_black#...
- bregma 7y agoWhen I visited Dublin that was the one spot I absolutely had to visit. For some folks it was the Temple Bar, for others the James Joyce trail. For me, it was the plaque on the Broombridge and the Trinity College Library.
- jchallis 7y agoFriesland (formerly part of Melitta) sells the kettle for about 37 euro. If you have a way to add the messaging, you are well on your way. https://frieslandversand.de/teekanne-1-4l-weiss-utah-teapot https://frieslandversand.de/teekanne-1-4l-weiss-utah-teapot
- Isamu 7y agoAny idea why the name Hamilton appears to be deliberately defaced on the inscription?
- kleer001 7y agoHahaha! That reminds me of the time I couldn't recall the name for "leaf blower" and called them an "air rake". If anyone's curious the story is here: https://en.wikipedia.org/wiki/Utah_teapot https://en.wikipedia.org/wiki/Utah_teapot
- CountHackulus 7y agoI explicitly made a detour when I was in Dublin to take a picture of it the plaque on that bridge. Worth it.
- chadcmulligan 7y agoIf you ever happen to be near a Siggraph the render man guys hand out little walking Utah teapots - a tradition going back many years apparently. Worth the price of admission :-)
- DonHopkins 7y agoThen you could dress up for Halloween as Broome Bridge!
- Koshkin 7y agoShe probably hoped for a different answer.
- tudelo 7y agoNo, I bet this was exactly the answer they were looking for. After all, it was love at first sight.
- xg15 7y ago> I answered, "i^2 = j^2 = k^2 = ijk = -1". Could you explain why? For someone without a math background, it seems indeed like a pretty arbitrary thing to define. (I can understand the idea behind complex numbers and how the multiplication rules followed from the desire to define the square root of a negative number - however, so far, I don't get the motivation of introducing even more "special" elements)
- Koshkin 7y agoSee, for example, https://math.stackexchange.com/questions/911807/what-is-the-motivation-for-quaternions/911814 https://math.stackexchange.com/questions/911807/what-is-the-...
- nilkn 7y agoBy the Frobenius theorem, there are only three possible structures for a real finite-dimensional associative division algebra. Those structures correspond to the real numbers, the complex numbers, and what are called the quaternions. So essentially the above definition is not arbitrary because it's the only other possible way (besides R and C) to get that sort of algebraic system. Of course, this is not obvious at all. C famously is algebraically closed as a field, which makes it a ripe playground for much of topology, algebraic geometry, and analysis. There are some nonobvious generalizations of algebraic closure for the quaternions. (Naively, the quaternions are not algebraically closed in the classic sense because, evidently, ix + xi - j has no root.) As for why one might want to consider such a noncommutative division algebra in the first place, the answer I suppose is just that it manages to pop up in a variety of areas in mathematics. We've already seen the connection with rotations in 3-space (the topic of this post). Here's another. The 3-sphere (that is, a sphere in 4-dimensional space whose surface is itself 3-dimensional) can be realized as the multiplicative group of unit quaternions spanned by {1,i,j,k}. Consider the circle H = {cos(theta) + i * sin(theta)} for real values of theta; H is a subset of the 3-sphere. If r is any unit quaternion, then the coset rH is another circle. But given a subgroup H of any group G, the left cosets of H in G form a partition of G. Therefore, these circles just described form a partition of all of the 3-sphere (the Hopf fibration). Speaking of rotations, the involvement of quaternions should not be surprising. Indeed, complex numbers are intimately involved in rotations in 2-space (multiplication by a unit complex number e^(i*theta) corresponds to rotation about the origin by theta). Quaternions can similarly express rotations in 3-space, but one cannot just left- or right-multiply but must instead use conjugation. In general, one can generalize this using the techniques of geometric algebra.
- jayshua 7y agoI’d probably go with “e^pi*i = -1”. Kinda cliched, but I really love that equation.
- Mathnerd314 7y agoThen you would have worry about the tau-ists: https://tauday.com/tau-manifesto https://tauday.com/tau-manifesto
- jayshua 7y agolol. I'm actually one of them. "e^tau*i=0" is my preferred form. I don't tend to bring it up because we're a little crazy and I don't want to draw attention to myself.
- evozer 7y agoshouldn't it be e^tau*i = 1 if tau is 2pi?
- jayshua 7y agoOops, typo. You're right. You could also write "e^tau*i = 1 + 0" to relate the "5 most important numbers in math" but that form always seemed a bit forced to me.
- nybble41 7y agoIf you write "-1 * e^(tau * i) + 1 = 0" you can reasonably claim to relate six important numbers: -1, e, tau, i, 1, and 0. IMHO that looks a bit less forced than the version with "1 + 0", though of course it's not the simplest form. (I mean, that "+ 0" could have been inserted almost anywhere...)
- Koshkin 7y agoOr, better yet, e^pi*i + 1 = 0. (My personal preference is E = mc^2.)
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- pastrami_panda 7y agoI love quaternions, but I have to ask: you'd rather have that formula than Euler's identity tattooed?
- klodolph 7y agoToday, mathematicians in the most general sense divide into algebraists and analysts. Tattooing Euler’s identity identifies you as a member of the analyst tribe, you live and breathe limits, sequences, and measures. A tattoo of Hamilton’s i^2 = j^2 = k^2 = ijk = -1 would identify you as a member of the algebraist tribe, who lives and breathes commutators, cohomologies, and quotients.
- pflats 7y agoThanks for writing this! It's spot on. I referenced it in a post upthread[1]. [1] https://news.ycombinator.com/item?id=22204995 https://news.ycombinator.com/item?id=22204995
- FisDugthop 7y agoAs another algebraist (category theory and computational complexity), this makes a lot of sense. Euler's identity is capricious and Euclidean to me, and far from the most beautiful equation, although it is still remarkably elegant. I don't have any tattoos, but I might consider some categorical diagram; I don't know how I'd pick just one! Perhaps there is some cool way to draw the Snake Lemma with a realistic-looking snake.
- uryga 7y ago> I don't know how I'd pick just one! picking one up to unique isomorphism should be good enough ;)
- tzs 7y agoIt's nice to see something other than e^(ᴨi)=-1. If I had to get a math tattoo, I think I'd go for lim n→∞ Q_n^(1/n) = e^(ᴨ^2/(12 log 2)). That comes from a theorem proved by Khinchin and Lévy. Khinchin proved that for almost all real numbers if you take the sequence of convergents of their continued fraction expansion, {P_1/Q_1, P_2/Q_2, ...}, then the sequence {Q_1, Q_2^(1/2), Q_3^(1/3), ...} approaches a limit, which is the same limit for almost all real numbers. Then Lévy determined the value of that limit, which is now called either Lévy's constant or the Khinchin–Lévy constant. If not that, then this (in standard math notation rather than the verbose notation I'm using here): Line 1: Let H_n = sum i=1 to n 1/n Line 2: Hypothesis: sum d|n d < H_n + e^H_n log(H_n) for all n > 1 That's neat because that hypothesis is true if and only if the Riemann hypothesis [1] is true [2]. The Riemann hypothesis is a conjecture about complex numbers, and is widely considered to be the most important unsolved problem in pure mathematics. That it turns out to be equivalent to a such a simple conjecture involving just integers and a couple real functions from pre-calculus is a surprise. [1] https://en.wikipedia.org/wiki/Riemann_hypothesis https://en.wikipedia.org/wiki/Riemann_hypothesis [2] https://arxiv.org/abs/math/0008177 https://arxiv.org/abs/math/0008177
- BlueTemplar 7y agoI'm curious about that "almost all" ?
- SamReidHughes 7y agoAll but a set with measure zero, in this case.
- BlueTemplar 7y agoWhy just not say "non-zero" then ?
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- logfromblammo 7y agoMine would be the Fano plane mnemonic for octonion multiplication, using two curves of constant width instead of the triangle and the circle. That's got the quaternions covered with the inside curve. It can go next to the skeletal formula for benzaldehyde on my imaginary nerd canvas.
- BlueTemplar 7y agoBrilliant !
- jtolmar 7y agoI'd probably pick the normal-normal conjugate prior, in precision form.