A convex polygon with n sides is drawn in a circle. Then divided into triangles. Finally circles are inscribed in the triangles. Obviously, triangulation is not unique; a 4-gon has two, a 5-gon five, a 6-gon 14 and so on, as continue the Catalan numbers. But the sum of the radii of the circles is constant, independent of how the n-gon is divided.

A convex polygon with n sides is drawn in a circle. Then divided into triangles. Finally circles are inscribed in the triangles. Obviously, triangulation is not unique; a 4-gon has two, a 5-gon five, a 6-gon 14 and so on, as continue the Catalan numbers. But the sum of the radii of the circles is constant, independent of how the n-gon is divided.

Notes

  1. joejoat reblogged this from visualizingmath
  2. colepierce reblogged this from colepierce
  3. vayuprana reblogged this from jakepalooka
  4. theartofmathematics reblogged this from mathani
  5. appleandkey reblogged this from visualizingmath
  6. recordmachine reblogged this from mathematica
  7. noxstopxandxxgo reblogged this from mathani
  8. pedalferrous reblogged this from visualizingmath and added:
    The sum of the radii is independent of the method of polygonal decomposition.
  9. riicequeen reblogged this from bragh-bragh-bree-bragh-bragh
  10. bragh-bragh-bree-bragh-bragh reblogged this from visualizingmath
  11. quotidian-ailee reblogged this from maddiebrandt
  12. goodmorningteachera reblogged this from visualizingmath
  13. infall-of-music reblogged this from curiosamathematica
  14. so-i-guess-i reblogged this from mathani
  15. irefiordiligi reblogged this from mathani
  16. hellblazer reblogged this from visualizingmath
  17. hiroshi-mod reblogged this from mathani
  18. clockworktea reblogged this from curiosamathematica
  19. ns-lion reblogged this from visualizingmath
  20. supehunter reblogged this from visualizingmath
  21. permademic reblogged this from mathani
  22. ponies-n-things reblogged this from jetn
  23. jetn reblogged this from visualizingmath
  24. gettothestabbing reblogged this from inquisitivition
  25. totorista reblogged this from visualizingmath
  26. alifewithout-timekeeping reblogged this from falling-drop-of-water
  27. pettytherapy reblogged this from visualizingmath