SOLUCIONES

Presentamos a continuación las respuestas [etapa.R#:Respuesta] de la mayoría de los problemas de esta primera Odi (por el momento omitimos aquellas que requieren gráficas o texto extenso). Compartimos simultáneamente algunas frases memorables. Que las disfruten. (nota: página en construcción)

  1. [I.R1: 23 y 24] I have discovered such wonderful things that I was amazed…out of nothing I have created a strange new universe —Janos Bolyai
  2. [I.R2: 14] Mountains are not cones, clouds are not spheres, trees are not cylinders, neither does lighting travel in a straight line. Almost everything around us is non-Euclidean. —Benoit Mandelbrot
  3. [I.R3: -6] If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven? —David Hilbert
  4. [I.R4: 1 grado] The laws of mathematics are not merely human inventions or creations. They simply “are”; they exist quite independently of the human intellect. The most that any man with a keen intellect can do is to find out that they are there and to take cognizance of them. —M. C. Escher
  5. [I.R5: sqrt(2)] … for no human inquiry can be called science unless it pursues its path through mathematical exposition and demonstration. —Leonardo da Vinci
  6. [I.R6: 29] We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori. —Karl Gauss
  7. [I.R7: 9] In any particular theory there is only as much real science as there is mathematics. —Immanuel Kant
  8. [I.R8: $16] Bees…by virtue of a certain geometrical forethought…know that the hexagon is greater than the square and the triangle and will hold more honey for the same expenditure of material. —Pappus of Alexandria
  9. [I.R9: 18] … the creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed. —Albert Einstein
  10. [I.R10: 22] The essence of mathematics is its freedom. —Georg Cantor
  11. [I.R11: 24]
  12. [I.R12: 10, 22, 26]
  13. [I.R13: 11]
  14. [I.R14: 260]
  15. [I.R15: 7]
  16. [I.R16: -8 (lb/in^2)/(in^3)]
  17. [II.R1: 30, -61]
  18. [II.R2: 324]
  19. [II.R3: (figura)]
  20. [II.R4: (texto)]
  21. [II.R5: 12, 8]
  22. [II.R6: 7/9]
  23. [II.R7: 3]
  24. [II.R8: 12, 15]
  25. [III.R1: A=16/15, K=-0.896]
  26. [III.R2: 9, 2, 2]
  27. [III.R3: (figura)]
  28. [III.R4: (texto)]
  29. [IV.R1: 1, ( ), ¿es de día?]
  30. [IV.R2: (a^(2/3) + b^(2/3))^(3/2)]

Actualizado: 2007.03.09 (nota: faltan algunas figuras y textos, además de las frases)