{"title":"3Blue1Brown","description":"\u003cmeta charset=\"utf-8\"\u003e\r\n\u003cp\u003e\u003cspan style=\"font-weight: 400;\"\u003e3blue1brown, by Grant Sanderson, is some combination of math and entertainment, depending on your disposition. The goal is for explanations to be driven by animations and for difficult problems to be made simple with changes in perspective.\u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp\u003e \u003c\/p\u003e","products":[{"product_id":"zeta-function-poster","title":"Zeta Function Poster","description":"\u003cmeta charset=\"utf-8\"\u003e\n\u003cp\u003e\u003cspan style=\"color: #0000ff;\"\u003e\u003cstrong\u003e$9.87 = π²\u003c\/strong\u003e\u003c\/span\u003e\u003c\/p\u003e\n\u003cp\u003e \u003c\/p\u003e","brand":"3Blue1Brown","offers":[{"title":"11\"x17\"","offer_id":40064616333466,"sku":"","price":11.9,"currency_code":"USD","in_stock":false},{"title":"18\"x24\"","offer_id":40064616366234,"sku":"E.2.16.02","price":14.9,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0571\/3195\/8426\/products\/zeta-function-poster.jpg?v=1623100464"},{"product_id":"fractal-curve-poster-set","title":"Fractal Curve Poster Set","description":"\u003ch2\u003e\u003cspan style=\"color: #0000ff;\"\u003e\u003cstrong\u003e﻿\u003c\/strong\u003e\u003cstrong\u003e$23.14 = exp(π)\u003c\/strong\u003e\u003c\/span\u003e\u003c\/h2\u003e\n\u003ch2\u003e\n\u003cspan style=\"color: #ff0000;\"\u003e\u003c\/span\u003e \u003c\/h2\u003e","brand":"3Blue1Brown","offers":[{"title":"Default Title","offer_id":40064616824986,"sku":"E.7.16.01 + E.7.16.02 + E.7.16.03","price":36.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0571\/3195\/8426\/products\/3blue1brown-pi-plushie.jpg?v=1623100466"},{"product_id":"pause-and-ponder-shirt","title":"Pause and Ponder Shirt","description":"\u003cmeta charset=\"utf-8\"\u003e\n\u003cp\u003e\u003cspan style=\"color: #0000ff;\"\u003e\u003cstrong\u003e$23.14 = exp(π)\u003c\/strong\u003e\u003c\/span\u003e\u003c\/p\u003e\n\u003cp\u003ePrinted on Next Level Apparel\u003c\/p\u003e","brand":"3Blue1Brown","offers":[{"title":"XS","offer_id":40064637567130,"sku":"Z.2.1.01-XS","price":26.0,"currency_code":"USD","in_stock":false},{"title":"S","offer_id":40064637599898,"sku":"Z.2.1.02-S","price":26.0,"currency_code":"USD","in_stock":false},{"title":"M","offer_id":40064637632666,"sku":"Z.2.1.03-M","price":26.0,"currency_code":"USD","in_stock":false},{"title":"L","offer_id":40064637665434,"sku":"Z.2.1.04-L","price":26.0,"currency_code":"USD","in_stock":false},{"title":"XL","offer_id":40064637698202,"sku":"Z.2.1.05-XL","price":26.0,"currency_code":"USD","in_stock":false},{"title":"XXL","offer_id":40064637730970,"sku":"Z.2.1.06-XXL","price":26.0,"currency_code":"USD","in_stock":false},{"title":"3XL","offer_id":40064637763738,"sku":"Z.2.1.07-3XL","price":26.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0571\/3195\/8426\/products\/pauseandpoder-site-1.jpg?v=1623100487"},{"product_id":"tall-3blue1brown-pi-plushie","title":"TALL 3Blue1Brown Pi Plushie","description":"\u003cmeta charset=\"utf-8\"\u003e\u003cmeta charset=\"utf-8\"\u003e\n\u003cp\u003e\u003cspan style=\"color: #0000ff;\"\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003c\/span\u003eContrary to popular perception, math is filled with character.  Numbers often seem to have personality, different fields are characterized as much by their style as by their content, and mathematicians themselves are often more enthusiastic about the beauty of their subject than artists.  On 3b1b, the pi creature has come to be a symbol of this unappreciated emotive quality in math, and the plushie pi is your chance to hold a physical reminder of this fact.\u003c\/p\u003e\n\u003cmeta charset=\"utf-8\"\u003e\n\u003cp\u003e Want the short version too? \u003ca href=\"https:\/\/store.dftba.com\/products\/short-3blue1brown-pi-plushie\"\u003eClick here!\u003c\/a\u003e\u003c\/p\u003e","brand":"3Blue1Brown","offers":[{"title":"Default Title","offer_id":40064647397530,"sku":"B.2.1.05","price":17.29,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0571\/3195\/8426\/products\/3blue1brown-pi-plushie_df42bd59-cea7-4a39-bd97-fe034b8058c7.jpg?v=1623100515"},{"product_id":"3blue1brown-sticker-set","title":"3blue1brown Sticker Set","description":"\u003cmeta charset=\"utf-8\"\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cspan style=\"color: #0000ff;\"\u003e$3.14 = π\u003c\/span\u003e\u003c\/strong\u003e  for 2 stickers\u003cbr\u003e\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cspan style=\"color: #0000ff;\"\u003e$9.87 = π\u003c\/span\u003e\u003c\/strong\u003e\u003cspan\u003e\u003cstrong\u003e\u003cspan style=\"color: #0000ff;\"\u003e²\u003c\/span\u003e\u003c\/strong\u003e  for 10 stickers\u003c\/span\u003e\u003c\/p\u003e\n\u003cp\u003eComes with two \u003cspan\u003ehex-compliment\u003c\/span\u003e standard stickers\u003c\/p\u003e\n\u003cp\u003ePurchase includes:\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003ePi Creature Sticker\u003c\/li\u003e\n\u003cli\u003e3blue1brown logo sticker\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e \u003c\/p\u003e\n\u003cp\u003e*LAST PRINTING*\u003c\/p\u003e","brand":"3Blue1Brown","offers":[{"title":"2 Pack (1 of each)","offer_id":40064679379098,"sku":"B.1.3B.18","price":3.14,"currency_code":"USD","in_stock":true},{"title":"10 Pack (5 of each)","offer_id":40064679411866,"sku":"C.4.4.08","price":9.87,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0571\/3195\/8426\/products\/3blue1brow-stickers-1.jpg?v=1623100564"},{"product_id":"3blue1brown-socks","title":"Fourier Series Socks","description":"\u003cmeta charset=\"utf-8\"\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cspan style=\"color: #0000ff;\"\u003e﻿\u003c\/span\u003e\u003c\/strong\u003e\u003cstrong\u003e\u003cspan style=\"color: #0000ff;\"\u003e\u003cspan\u003e$12.56 = 4π\u003c\/span\u003e\u003c\/span\u003e\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp\u003e\u003cspan\u003eThese socks show various periodic functions, as graphed on a cylinder, the way all periodic functions wish they were graphed.  Specifically, they show the first few Fourier series approximations of a square wave.\u003c\/span\u003e\u003c\/p\u003e\n\u003cp\u003eEach order comes with one pair of socks.\u003c\/p\u003e\n\u003cp\u003eSize Medium fits women's shoe sizes 6 to 9.5.\u003c\/p\u003e\n\u003cp\u003eSize Large fits men's shoe sizes 8 to 12.5. \u003c\/p\u003e\n\u003cmeta charset=\"utf-8\"\u003e\n\u003cdiv\u003eAbout 60% cotton, 35% nylon, 5% spandex\u003c\/div\u003e\n\u003cdiv\u003e\u003c\/div\u003e","brand":"3Blue1Brown","offers":[{"title":"M","offer_id":40064694517914,"sku":"Z.5.4.12-M","price":12.56,"currency_code":"USD","in_stock":true},{"title":"L","offer_id":40064694550682,"sku":"Z.5.4.13-L","price":12.56,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0571\/3195\/8426\/products\/fourier-socks-1.png?v=1623100581"},{"product_id":"short-3blue1brown-pi-plushie","title":"SHORT 3Blue1Brown Pi Plushie","description":"\u003cmeta charset=\"utf-8\"\u003e\u003cmeta charset=\"utf-8\"\u003e\u003cmeta charset=\"utf-8\"\u003e\n\u003cp\u003e\u003cspan style=\"color: #0000ff;\"\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003c\/span\u003eContrary to popular perception, math is filled with character.  Numbers often seem to have personality, different fields are characterized as much by their style as by their content, and mathematicians themselves are often more enthusiastic about the beauty of their subject than artists.  On 3b1b, the pi creature has come to be a symbol of this unappreciated emotive quality in math, and the plushie pi is your chance to hold a physical reminder of this fact.\u003c\/p\u003e\n\u003cp\u003e Want the tall version too? \u003ca href=\"https:\/\/store.dftba.com\/products\/tall-3blue1brown-pi-plushie\"\u003eClick here!\u003c\/a\u003e\u003c\/p\u003e","brand":"3Blue1Brown","offers":[{"title":"Default Title","offer_id":40064695828634,"sku":"C.1.3.01","price":17.29,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0571\/3195\/8426\/products\/3blue1brown-pi-plushie-SHORT-1.jpg?v=1623100583"},{"product_id":"eulers-characteristic-mug","title":"Euler's Characteristic Mug","description":"\u003cmeta charset=\"utf-8\"\u003e\n\u003cp\u003e\u003cspan style=\"color: #0000ff;\"\u003e\u003cstrong\u003e$9.87 = π²\u003c\/strong\u003e\u003c\/span\u003e\u003c\/p\u003e\n\u003cp\u003e11oz white ceramic mug with wrap around printing. Hand-wash only recommended.\u003c\/p\u003e\n\u003cp\u003eTake your favorite spherical object lying around –an orange, a tennis ball, whatever– and cover it with dots.  Now draw a bunch of lines connecting these dots, being careful never to let the lines cross.  In effect, you're drawing a polyhedron whose faces have been warped onto the surface of your sphere.  Add up the number of dots (verticies), subtract the number of lines (edges), and add the number of faces you've divided the surface into, and you'll always get 2.  No matter what dots and lines you chose to draw!  The object doesn't even have to be a sphere.  If you're comfortable drawing all over the surface of your laptop, you'd find the same thing:  V - E + F = 2.  This is Euler's characterisic formula.\u003c\/p\u003e\n\u003cp\u003e \u003c\/p\u003e\n\u003cdiv\u003e\"But wait,\" I hear you say, \"you've misprinted the formula on the mug!\"  Quite the contrary, my friend.  If you were to play this same game on the surface of a mug you'd find that the formula changes.  Instead, as you add the vertices subtract the edges and add the faces, you'd always get 0.  Likewise if you tried this on a bagel, or any other surface which has one hole in it.  Or rather, this is true as long as none of the faces you draw end up with a hole.  So you'd have to make sure some of your drawing happens on the handle, for example.  This expression, V - E + F, is a sort of topological fingerprint for a surface. You may have heard that to a topologist, a mug and a doughnut are the same thing, in the sense that one can be continuously deformed to make the other.  The fact that V - E + F = 0 on both these surfaces is one way to make this similarity something a bit more quantitative, and hence something you can actually use for computations and proofs.\u003c\/div\u003e\n\u003cdiv\u003e\u003c\/div\u003e\n\u003cdiv\u003eYou can find a description of Euler's formula in \u003ca href=\"https:\/\/www.youtube.com\/watch?v=VvCytJvd4H0\u0026amp;feature=youtu.be\"\u003ethis video\u003c\/a\u003e.  My challenge to you is to take the argument in that video, and think through what changes on surfaces with a hole, like a doughnut or a mug.  If you do wrap your mind around it, you'll find that this is a remarkably clever way to codify the idea of how many \"holes\" a surface has in it.  And if you feel the need to get emperical with an actual mug, I know of a place where you can buy one...\u003c\/div\u003e\n\u003cmeta charset=\"utf-8\"\u003e\u003cmeta charset=\"utf-8\"\u003e\n\u003cdiv\u003e\u003c\/div\u003e","brand":"3Blue1Brown","offers":[{"title":"Default Title","offer_id":40064709329050,"sku":"A.2.4.02","price":16.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0571\/3195\/8426\/products\/eulers-formula-mug.jpg?v=1623100607"},{"product_id":"3blue1brown-vertical-alignment-shirt","title":"3Blue1Brown Vertical Alignment Shirt","description":"\u003cmeta charset=\"utf-8\"\u003e\u003cmeta charset=\"utf-8\"\u003e\n\u003cp\u003e\u003cspan style=\"color: #0000ff;\"\u003e\u003cstrong\u003e$23.14 = exp(π)\u003c\/strong\u003e\u003c\/span\u003e\u003c\/p\u003e\n\u003cp\u003e\u003cspan style=\"color: #0000ff;\"\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003c\/span\u003ePrinted on Next Level Apparel \u003c\/p\u003e\n\u003cmeta charset=\"utf-8\"\u003e\n\u003cp\u003e\u003cspan\u003e60% Combed Ring-Spun Cotton 40% Polyester\u003c\/span\u003e\u003c\/p\u003e\n\u003cp\u003e \u003c\/p\u003e","brand":"3Blue1Brown","offers":[{"title":"Unisex \/ XS","offer_id":40064724500634,"sku":"W.8.3.08-XS","price":26.0,"currency_code":"USD","in_stock":true},{"title":"Unisex \/ S","offer_id":40064724533402,"sku":"W.8.3.09-S","price":26.0,"currency_code":"USD","in_stock":true},{"title":"Unisex \/ M","offer_id":40064724566170,"sku":"W.8.3.10-M","price":26.0,"currency_code":"USD","in_stock":true},{"title":"Unisex \/ L","offer_id":40064724631706,"sku":"W.8.3.11-L","price":26.0,"currency_code":"USD","in_stock":true},{"title":"Unisex \/ XL","offer_id":40064724697242,"sku":"W.8.3.12-XL","price":26.0,"currency_code":"USD","in_stock":true},{"title":"Unisex \/ XXL","offer_id":40064724762778,"sku":"W.8.3.13-XXL","price":26.0,"currency_code":"USD","in_stock":true},{"title":"Unisex \/ 3XL","offer_id":40064724828314,"sku":"W.8.3.14-3XL","price":26.0,"currency_code":"USD","in_stock":true},{"title":"Curved \/ XS","offer_id":40064724893850,"sku":"X.8.3.01-XS","price":26.0,"currency_code":"USD","in_stock":true},{"title":"Curved \/ S","offer_id":40064724926618,"sku":"X.8.3.02-S","price":26.0,"currency_code":"USD","in_stock":true},{"title":"Curved \/ M","offer_id":40064724992154,"sku":"X.8.3.03-M","price":26.0,"currency_code":"USD","in_stock":true},{"title":"Curved \/ L","offer_id":40064725090458,"sku":"X.8.3.04-L","price":26.0,"currency_code":"USD","in_stock":true},{"title":"Curved \/ XL","offer_id":40064725155994,"sku":"X.8.3.05-XL","price":26.0,"currency_code":"USD","in_stock":true},{"title":"Curved \/ XXL","offer_id":40064725221530,"sku":"X.8.3.06-XXL","price":26.0,"currency_code":"USD","in_stock":true},{"title":"Curved \/ 3XL","offer_id":40064725287066,"sku":"X.8.3.07-3XL","price":26.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0571\/3195\/8426\/products\/vertical-3blue1brown-site-1.jpg?v=1623100625"},{"product_id":"zeta-spiral-shirt","title":"Zeta Spiral Shirt","description":"\u003cmeta charset=\"utf-8\"\u003e\u003cmeta charset=\"utf-8\"\u003e\n\u003cp\u003e\u003cspan style=\"color: #0000ff;\"\u003e\u003cstrong\u003e$23.14 = exp(π)\u003c\/strong\u003e\u003c\/span\u003e\u003c\/p\u003e\n\u003cp\u003ePrinted on Next Level Apparel \u003c\/p\u003e\n\u003cp\u003e60% Combed Ring-Spun Cotton 40% Polyester\u003c\/p\u003e\n\u003cmeta charset=\"utf-8\"\u003e\n\u003cp\u003eThe Riemann zeta function is the object for one of the most famous unsolved problems in math, the Riemann Hypothesis.  It's a big enough deal, in fact, to have a $1,000,000 prize offered for its resolution from the Clay Math Institute, although the money probably pales in importance compared to the mark you would make in mathematical history by resolving it.  3blue1brown viewers may be familiar with \u003ca href=\"https:\/\/www.youtube.com\/watch?v=sD0NjbwqlYw\u0026amp;feature=youtu.be\"\u003ethis video\u003c\/a\u003e walking through how the function itself is defined.  The million dollar question is whether all \"non-trivial zeros\" of this funciton lie on the line 0.5 + it, where t ranges over all real numbers.  This is the so-called \"critical line\".\u003cbr\u003e\u003cbr\u003eIllustrated on this shirt is the chaotic behavior of the zeta function on this critical line (for t ranging from 0 to 50, if you're curious), as animated \u003ca href=\"https:\/\/www.youtube.com\/watch?v=sD0NjbwqlYw\u0026amp;feature=youtu.be\u0026amp;t=1130\"\u003ehere\u003c\/a\u003e.  Why do mathematicians care?  Each point where this spiraling line crosses zero corresponds, in some sense, to a prominant frequency in the pattern of prime numbers, making the collection of these zeros something like a musical chord which encodes patterns in the primes, and no one fully understands it.\u003cbr\u003e\u003cbr\u003eAnd tell you what, if you do solve the Riemann hypothesis, I'll send you a free shirt.\u003c\/p\u003e","brand":"3Blue1Brown","offers":[{"title":"Unisex \/ XS","offer_id":40064726335642,"sku":"X.6.1.01-XS","price":23.14,"currency_code":"USD","in_stock":false},{"title":"Unisex \/ S","offer_id":40064726368410,"sku":"X.6.1.02-S","price":23.14,"currency_code":"USD","in_stock":false},{"title":"Unisex \/ M","offer_id":40064726401178,"sku":"X.6.1.03-M","price":23.14,"currency_code":"USD","in_stock":false},{"title":"Unisex \/ L","offer_id":40064726433946,"sku":"X.6.1.04-L","price":23.14,"currency_code":"USD","in_stock":false},{"title":"Unisex \/ XL","offer_id":40064726466714,"sku":"X.6.1.05-XL","price":23.14,"currency_code":"USD","in_stock":false},{"title":"Unisex \/ 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