Atomism and Infinite Divisibility


  1. Subjective-Objective dimension.
  2. Visual apparatus involved in the minimum perceptual experience.
  3. Dividing a line of unknown length into equal parts.
  4. Continuous Metric inscribed squares.
  5. Atomic metric inscribed squares.
  6. Similar triangle perceptual argument.
  7. A long thin triangle only two atoms high on one end.
  8. A 7x7 square with one diagonal drawn on an atomic array.
  9. Square, Display, and Print aspect ratios.
  10. The two sides of a line.
  11. Using the rightmost and lower points to fill out a line.
  12. Adding lengths of line segments.
  13. Line segments which cross but do not share a point of intersection.
  14. Points selected for thickening a line to the left.
  15. Points selected for thickening a line to the right.
  16. A degenerate atomic triangle.
  17. The minimum sized atomic triangle.
  18. Locating vertex points of a continuous triangle on atomic points.
  19. Locating the vertices of a right atomic triangle.
  20. Filing in the base and height of an atomic right triangle.
  21. Filing in the interior points of an atomic right triangle.
  22. Similar continuous triangles.
  23. Table of areas for selected atomic triangles.
  24. Various small atomic triangles.
  25. A square with one diagonal.
  26. A square with sides of length C inscribed inside another square.
  27. Pictorial representation of area computation for an atomic triangle with an even base.
  28. Squares in the atomic plane without square areas.
  29. The area of the diagonal in atomic isosceles triangles.
  30. Intersection points of 4 triangles.
  31. Illustrating the equivalent of the Pythagorean proof figure with atomic figures.
  32. A 5x5 square rotated 45 and superimposed on a diagonal square with an area of 25 atomic units.
  33. Atomic Pythagorean theorem demonstration for the case of A=3, B=4, and C=4.