{"product_id":"vector-field-socks","title":"Vector Field Socks","description":"\u003cmeta charset=\"utf-8\"\u003e\n\u003cp\u003eBased on \u003ca href=\"https:\/\/youtu.be\/p_di4Zn4wz4\"\u003ethis\u003c\/a\u003e video:\u003c\/p\u003e\n\u003cp\u003eA classic example for student of differential equations is the non-linear pendulum. These socks illustrate what's known as the \"phase space\" of that system (see the video above), but represented on a cylinder, which is much more natural than most other diagrams you'll find. \u003cbr\u003eOne axis represents the angle of the pendulum, and the other represents angular velocity.  But that angle is cyclic; rotating the pendulum 360 degrees doesn't change how it looks.  So the most honest phase space of this pendulum should have this x-axis wrapping round onto itself, as it does on these socks.\u003cbr\u003eThe white spiral in this diagram shows a typical trajectory for a pendulum, slowly rotating back and forth as it looses energy and tends towards a state where the angle and angular velocity are both zero.\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":40064748880026,"sku":"Z.4.1.08-M","price":12.56,"currency_code":"USD","in_stock":true},{"title":"L","offer_id":40064748912794,"sku":"Z.4.1.09-L","price":12.56,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0571\/3195\/8426\/products\/pendulum-socks-1.jpg?v=1623100679","url":"https:\/\/dftbasandbox.myshopify.com\/products\/vector-field-socks","provider":"DFTBAsandbox","version":"1.0","type":"link"}