Skip to Navigation | Skip to Content

think4yourself

1ucasvb:

The familiar trigonometric functions can be geometrically derived from a circle. But what if, instead of the circle, we used a regular polygon? In this animation, we see what the “polygonal sine” looks like for the square and the hexagon. The polygon is such that the inscribed circle has radius 1. (There’s a very neat reason for this.) Since these polygons are not perfectly symmetrical like the circle, the function will depend on the orientation of the polygon. More on this subject and derivations of the functions can be found in this other post
Now you can also listen to what these waves sound like
This technique is general for any polar curve. Here’s a heart’s sine function, for instance

1ucasvb:

The familiar trigonometric functions can be geometrically derived from a circle. But what if, instead of the circle, we used a regular polygon? In this animation, we see what the “polygonal sine” looks like for the square and the hexagon. The polygon is such that the inscribed circle has radius 1. (There’s a very neat reason for this.) Since these polygons are not perfectly symmetrical like the circle, the function will depend on the orientation of the polygon. More on this subject and derivations of the functions can be found in this other post

Now you can also listen to what these waves sound like

This technique is general for any polar curve. Here’s a heart’s sine function, for instance

All Notes

  1. ghostprinxe reblogged this from anubimon
  2. thefatdrake reblogged this from sketchyraviel
  3. stefiman reblogged this from sketchyraviel
  4. sketchyraviel reblogged this from shadowplier
  5. passiveintellect reblogged this from hitchin-a-ride-to-suburbia
  6. florenciabitch02 reblogged this from legit-humour
  7. that-weird-akward-girl reblogged this from crimsoncamellianeko
  8. aradian reblogged this from lira2602
  9. veeshnyah reblogged this from crashpl
  10. the-sweet-nonsense reblogged this from a-little-ray-of-fantasy
  11. lira2602 reblogged this from intelark
  12. ohmytgot reblogged this from warmaster-seerus
  13. hazelroselove reblogged this from katherinelockewood
  14. a-little-ray-of-fantasy reblogged this from puccafangirl
  15. flyingkittengirl reblogged this from actualrigel
  16. intelark reblogged this from actualrigel
  17. elysiandulcinea reblogged this from darkimber
  18. be-true2whouare reblogged this from getl0stwithy0u
  19. oliverthepanda reblogged this from jaskierpl
  20. darkimber reblogged this from mariamoonfang
  21. minid97 reblogged this from shablamski
  22. marzley-kazmark reblogged this from irlbunny
  23. biboyfromvb reblogged this from jaskierpl