Online catalogue of Archimedean circles

Archimedean circles are circles in the arbelos, congruent to the Archimedean twin circles and with relevant additional properties.

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Archimedean circles

  1. Archimedean circles 1a and 1b: The Archimedean twins

  2. Archimedean circle 2: Bankoff's triplet circle

  3. Archimedean circle 3: Bankoff's quadruplet circle

  4. Archimedean circle 4: Reflection of Bankoff's quadruplet circle

  5. Archimedean circles 5a and 5b: The cousin circles

  6. Archimedean circle 6: The C-circle

  7. Archimedean circles 7a and 7b: The 2nd and 3rd rectangle circles

  8. Archimedean circle 8: The 4th rectangle circle

  9. Archimedean circle 9: The Dearing circle

  10. Archimedean circles 10a and 10b: The Schoch twins

  11. Archimedean circle 11: The Schoch incircle

  12. Archimedean circle 12: The Schoch-Woo circle

  13. Archimedean circle 13: The first Schoch line circle

  14. Archimedean circle 14: The second Schoch line circle

  15. Archimedean circle 15: The Schoch segment circle

  16. Archimedean circle 16: The midpoint reflection of Bankoff's triplet circle

  17. Archimedean circle 17: The midpoint line reflection of Bankoff's triplet circle

  18. Archimedean circle 18: Fourth symmetry of Bankoff's triplet circle

  19. Archimedean circles 19a and 19b: The Schoch intersection point Circles

  20. Archimedean circles 20a and 20b: The lifted Cousin Circles

  21. Archimedean circle 21: The Schoch Tangent Circle

  22. Archimedean circle 22: The Yiu-Woo Circle

  23. Archimedean circle 23: The Yiu-Schoch Circle

  24. Archimedean circles 24a, 24b, 24c, 24d: The Power circles

  25. Archimedean circles 25a and 25b: The Midway semicircle circles

  26. Archimedean circle 26: The Yiu circle

  27. Archimedean circle 27: First reflection of the Triplet circle

  28. Archimedean circle 28: Second reflection of the Triplet circle

  29. Archimedean circles 29a and 29b: The first Radical line pair

  30. Archimedean circles 30a and 30b: The 2nd Radical line pair

  31. Archimedean circles 31a and 31b: The midarc circle pair

  32. Archimedean circles 32a and 32b: The MC circles

  33. Archimedean circles 33a and 33b: Brothers of the quadruplet circles

  34. Archimedean circles 34a and 34b: Older Twins

  35. Archimedean circle 35: The Schoch-Flower circle

  36. Archimedean circles 36a and 36b: The congruent inversion image circles

  37. Archimedean circles 37a and 37b: The Schoch line tangent circles

  38. Archimedean circles 38a, 38b, 38c, 38d: The CD-circle Powerian pairs

  39. Archimedean circles 39a, 39b, 39c, 39d: The O' Powerian pairs
  40. Archimedean circles 40a, 40b, 40c, 40d: The Outside Powerian Pairs
  41. Archimedean circle 41: Reflection of Triplet circle through O'
  42. Archimedean circles 42a and 42b: QTB circles
  43. Archimedean circle 43: Reflection of (A16) through M
  44. Archimedean circles 44a and 44b: First QTB Powerian pair
  45. Archimedean circles 45a and 45b: Second QTB Powerian pair
  46. Archimedean circles 46a, 46b, 46c, 46d: The Common tangent quadruple
  47. Archimedean circles 47a and 47b: The eyeball pair
  48. Archimedean circle 48: External Okumura-Watanabe circle
  49. Archimedean circle 49: Orthogonal Okumura Watanabe circle
  50. Archimedean circles 50a and 50b: The 50th pair
  51. Archimedean circles 51a, 51b, 51c, 51d, 51e, 51f, 51g and 51h: The insquare octet
  52. Archimedean circles 52a, 52b, 52c, 52d: Cousins of the Second QTB Powerian Pair

  53. Archimedean circles 53a and 53b: Neighbourcouple of the Second QTB Powerian Pair
  54. Archimedean circles 54a and 54b: The O-basal pair
  55. Archimedean circles 55a and 55b: Outside basal pair
  56. Archimedean circle 56: Inverse of O'-line in (CD)
  57. Archimedean circles 57a and 57b: The Belev-pair
  58. Archimedean circles 58a and 58b: The Bui chords circles
  59. Archimedean circles 59a and 59b: First García pair
  60. Archimedean circles 60a and 60b: Second García pair
  61. Archimedean circles 61a and 61b: Dao pair
  62. Archimedean circle 62: Sanchez-García triplet circle

References

  1. L. Bankoff, A Mere Coincidence, Mathematics Newsletter, Los Angeles City College, Nov. 1954; reprinted in Coll. Math. J., 23 (1992) 106.
  2. L. Bankoff, Are the Twin Circles of Archimedes Really Twins?, Math. Mag., 47 (1974) 214--218.
  3. D. Belev, A Generalization of the Classical Arbelos and the Archimedean Circles, Mathematics plus, volume 16 (64) (2008) 4:54--68.
  4. Q.T. Bui, The Arbelos and Nine-Point Circles, Forum Geometricorum, 7 (2007) 115--120.
  5. E. Danneels and F.M. van Lamoen, Midcircles and the Arbelos, Forum Geometricorum, 7 (2007) 53--65.
  6. C.W. Dodge, T. Schoch, P.Y. Woo and P. Yiu, Those Ubiquitous Archimedean Circles, Math. Mag., 72 (1999) 202--213. Download
  7. I. d'Ignazio and E. Suppa, Il Problema Geometrico, dal Compasso al Cabri, Interlinea Editrice, Téramo, 2001.
  8. H. Okumura, Lamoenian Circles of the Collinear Arbelos, KoG, 17 (2013) 9--13.
  9. H. Okumura and M. Watanabe, The Archimedean Circles of Schoch and Woo, Forum Geometricorum, 4 (2004) 27--34.
  10. H. Okumura and M. Watanabe, Characterizations of an Infinite Set of Archimedean Circles, Forum Geometricorum, 7 (2007) 121--123. (a)
  11. H. Okumura and M. Watanabe, Remarks on Woo's Archimedean Circles, Forum Geometricorum, 7 (2007) 125-128. (b)
  12. F.M. van Lamoen, Archimedean Adventures, Forum Geometricorum, 6 (2006) 79--96.
  13. F.M. van Lamoen, Some Powerian pairs in the arbelos, Forum Geometricorum, 7 (2007) 111--113.
  14. F. Power, Some More Archimedean Circles in the Arbelos, Forum Geomectricorum, 5 (2005) 133--134.
  15. P. Yiu, The Archimedean Circles in the Shoemaker's Knife, lecture at the annual meeting of the Florida Section of the Mathematical Association of America, 1998.
  16. A. Wendijk, Problem 10895, Amer. Math. Monthly, solution by T. Hermann, 110 (2003) 63--64.

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