Math Tattoo Ideas

Math Tattoo Ideas Hey folks only a short kind of out of the ordinary video for you today a pal of mine cam lately got a math tattoo it's not something I recommend but he told his squad at work that if they reached a certain stretch destination it's something that he does and while the motivation operated cams initials are CSC which happens to be the shorthand for the cosecant function in trigonometry so what he decided to do is acquire his tattoo any particular geometric the representatives from what that run necessitates its kind of like a wordless signature writes to pure math they get me reckoning though about why on land we teach students about the trigonometric runs cosecant secant and cotangent and it occurred to me that there's something kind of poetic about this particular tattoo just as tattoos are artificially painted on but become permanent as though it.

Math Tattoo Ideas

We're a core part of funding recipients flesh the facts of the case that the cosecant is a called run is kind of an artificial erect on soul trigonometry could just as well have existed intact without the cosecant never being called out because it was it has this strange and artificial immortality in our conventions and to some extent in our education system in other statements the cosecant was not a tattoo on cams chest it's a tattoo on map itself something which seemed reasonable and even worthy of afterlife revises inception but which doesn't inevitably hold up as period runs on here let me actually depict you all a picture of the tattoo that he choice because not a lot of people know that geometric representation of the cosecant whenever you have an inclination normally represented with the Greek letter theta it's common in trigonometry to related to a corresponding moment on the human rights unit clique the clique with a radius one centered at the descent in the XY-plane most trigonometry students learned that the distance between this moment here on the clique and the x-axis is the sine of the inclination.

The distance between that moment and the y-axis is the cosine of the inclination and these connections make a really amazing understanding for what cosine and sine are all about people might learn that the tangent of an inclination is signed divided by cosine and that the cotangent is the other way around cosine/ sign but relatively few learned that there's also a nice geometric version for each of those lengths if you draw a line tangent to the clique at this moment the distance from that point to the x-axis along that tangent is well the tangent of the inclination and the distance along that line to the moment where it smacks the y-axis well that's the cotangent of the inclination again this demonstrates a really intuitive feel for what those lengths mean you kind of reckon tweaking that theta and viewing when cotangent get smaller excited and get larger and it's a check for any students working with them likewise secant which is defined as 1 divided by the cosine and cosecant which is defined as 1 divided by the sine of theta each have their own residences on this diagram if you look at that point where this tangent line bridges the x-axis the distance from that point to the descent is the secant of the inclination that is one divided by the cosine likewise the distance between where this tangent line bridges the y-axis.

The descent is the cosecant of the inclination would make good math tattoo ideas that is one divided by the sine if you're wondering why on land that's true notice that we have two similar right triangles here one small one inside the clique and this larger triangle whose hypotenuse is resting on the y-axis I'll leave it to you to check that interior inclination up at the tip-off here I am theta the inclination that we originally started with over inside the clique now for each one of those triangles I require you to think about the ratio of the duration of the side opposite theta to the duration of the hypotenuse for the small triangle the length of the opposite side is sine of theta and the hypotenuse is that radius the one that we define to have duration 1 so the rate is just sine of theta divided by 1 now when we looking at "the worlds largest" triangle the side opposite theta is that radio line of duration 1 and the hypotenuse is now this duration on the y-axis the one that I'm claiming is the cosecant if you take the reciprocal of each side here you see that this matches up with the fact that the cosecant of theta is 1 divided by sine kinda refrigerate right it's also kind of nice that sign tangent and secant all corresponding duration of positions that somehow "re going to the" x-axis and then the corresponding cosine cotangent and cosecant are all the segments of positions going to the matching places on the y-axis and on a diagram like this are liable to be pleasing that all six of these are separately called runs but in any practical use of trigonometry you can get by only utilizing sine cosine and tangent in fact if you really with math tattoo ideas.

That cosine and tangent correspond to come up regularly enough that it's more convenient to give them their own calls but cosecant secant and cotangent never genuinely come up in problem solving in a mode that's not just as convenient to write in terms of sine cosine and tangent at that point it's really only lending more statements for students to memorize with not that much lent utility and if anything if you merely acquainted secant is 1 over cosine and cosecant is 1 over sine the mismatch of this code prefix is probably just an added moment of embarrassment in a class that's prone enough to embarrassment for many of its students the reason that all six members of these functions have separate calls by the mode is that before information technology and calculators if you were doing trigonometry perhaps because your sailor Math Tattoo Ideas or an astronome Math Tattoo Ideas or some kind of engineer you'd find the values for these runs utilizing large-scale maps that only registered known input-output pairs and when you can easily plug in something like 1 divided by the sine of 30 degrees into a calculator it might actually acquire sense to have a dedicated article to this cost with a dedicated call and if you have a diagram like this one in psyche when you're taking measurements with sign tangent and secant having nicely reflected gists to co-sign cotangent cosecant calling this cosecant instead of 1 divided by sine might actually acquire some sense and it might actually make it easier to remember what it necessitates geometrically but hours have changed and most use instances for trig only don't involve maps of values and diagrams like this hence the cosecant and its brothers are tattoos on math opinions who's immortality in our meetings is our own doing not research results of nature itself and in general I actually think this is a good lesson for any tattoo lover memorizing a new portion of math at whatever tier you only got to take a moment and ask yourself whether what you're learning is core to the flesh of math itself into nature itself or if what you're looking at is actually only inked onto the subject and could just as readily have been inked on and some entirely other mode before you go I've got a journal recommendations regarding you symbolize principally for those of you who don't already listen to audiobooks you see this video help support audible.com which as many of you know affords audio works and other audio the documentation and if you go to audibletrial.com/ 3blue1brown free trial sense you can listen to pretty much whatever it is you require for free today I recomment Math Tattoo Ideas zen and the artistry of motorcycle upkeep this is actually what i listen to right after the artistry of memorizing exactly what i recommends the following to you guys at the end of the last video on the zeta function since the author of the artistry of memorizing was actually a big fan of zen and the artistry of motorcycle upkeep actually i ceased up listening to it twice since it's just that kind of journal it's very unusual in a mode that seems neither like fiction or nonfiction it's really theoretical and very thought-provoking but at the same period it's a powerful lesson and empathy and storytelling.