Constructing ovals, ovoids and spirals

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Constructing ovals, ovoids and spirals

  1. 1. Constructing ovals,ovoids and spirals
  2. 2. Draw an oval knowing thelenght of axes AB and CD
  3. 3. Draw an arc with its center at O and with radius of OA that intersects the extension of CD (minor axis) at point P. Join points A and C. C A O B D
  4. 4. Draw an arc with its center at O and with radius of OA that intersects the extension of CD (minor axis) at point P. Join points A and C. C A O B D
  5. 5. Draw an arc with its center at O and with radius of OA that intersects the extension of CD (minor axis) at point P. Join points A and C. 0° 179 C A O B D
  6. 6. Draw an arc with its center at O and with radius of OA that intersects the extension of CD (minor axis) at point P. Join points A and C. C 179 0° A O B D
  7. 7. Draw an arc with its center at O and with radius of OA that intersects the extension of CD (minor axis) at point P. Join points A and C. P C A O B D
  8. 8. Draw an arc with its center at O and with radius of OA that intersects the extension of CD (minor axis) at point P. Join points A and C. P C A O B D
  9. 9. Draw an arc with radius CP and the centre on C until it intersects segment AC at V. P C A O B D
  10. 10. Draw an arc with radius CP and the centre on C until it intersects segment AC at V. P 58 0° C A O B D
  11. 11. Draw an arc with radius CP and the centre on C until it intersects segment AC at V. 131° 58 P 58 0° C A O B D
  12. 12. Draw an arc with radius CP and the centre on C until it intersects segment AC at V. 131° 58 P 58 0° C A O B D
  13. 13. Draw an arc with radius CP and the centre on C until it intersects segment AC at V. 131° 58 P 58 0° C V A O B D
  14. 14. Draw an arc with radius CP and the centre on C until it intersects segment AC at V. 131° 58 P 58 0° C V A O B D
  15. 15. Draw its perpendicular bisector AV, wich willintersect OD or its extension at point M, as well as the major semiaxis at point N. P C V A O B D
  16. 16. Draw its perpendicular bisector AV, wich willintersect OD or its extension at point M, as well as the major semiaxis at point N. 0° 91 P C V A O B D
  17. 17. Draw its perpendicular bisector AV, wich willintersect OD or its extension at point M, as well as the major semiaxis at point N. 0° 91 0° 91 P C V A O B D
  18. 18. Draw its perpendicular bisector AV, wich willintersect OD or its extension at point M, as well as the major semiaxis at point N. 0° 91 0° 91 P C V 0° 91 A O B D
  19. 19. Draw its perpendicular bisector AV, wich willintersect OD or its extension at point M, as well as the major semiaxis at point N. 0° 91 0° 91 P C V 0° 91 A O B D
  20. 20. Draw its perpendicular bisector AV, wich willintersect OD or its extension at point M, as well as the major semiaxis at point N. 0° 91 0° 91 P C V 0° 91 A O B D
  21. 21. Draw its perpendicular bisector AV, wich willintersect OD or its extension at point M, as well as the major semiaxis at point N. 0° 91 0° 91 P C V 0° 91 N A O B D M
  22. 22. Draw its perpendicular bisector AV, wich willintersect OD or its extension at point M, as well as the major semiaxis at point N. 0° 91 0° 91 P C V 0° 91 N A O B D M
  23. 23. Draw the symmetrical points of M and N on the opposite ide of the axes, M’ and N’. P C V N A O B D M
  24. 24. Draw the symmetrical points of M and N on the opposite ide of the axes, M’ and N’. P C V N A O B 140 0° D M
  25. 25. Draw the symmetrical points of M and N on the opposite ide of the axes, M’ and N’. 0° P 86 C V N A O B 140 0° D M
  26. 26. Draw the symmetrical points of M and N on the opposite ide of the axes, M’ and N’. 0° P 10° 86 86 C V N A O B 140 0° D M
  27. 27. Draw the symmetrical points of M and N on the opposite ide of the axes, M’ and N’. 0° P 10° 86 M 86 C V N N A O B 140 0° D M
  28. 28. Join points M and M’ to N and N’ and draw arcswith centres M’ and M and with radius M’D and MC. P M C V N N A O B D M
  29. 29. Join points M and M’ to N and N’ and draw arcswith centres M’ and M and with radius M’D and MC. P M C V N N N A O B D M
  30. 30. Join points M and M’ to N and N’ and draw arcswith centres M’ and M and with radius M’D and MC. P M C C V N N N A O B D M
  31. 31. Join points M and M’ to N and N’ and draw arcswith centres M’ and M and with radius M’D and MC. P M C C V N N N A O B D M
  32. 32. Join points M and M’ to N and N’ and draw arcswith centres M’ and M and with radius M’D and MC. P M C C V N N N A O B D M
  33. 33. Join points M and M’ to N and N’ and draw arcswith centres M’ and M and with radius M’D and MC. P M C C V N N N A 0° 257 O B D M
  34. 34. Join points M and M’ to N and N’ and draw arcswith centres M’ and M and with radius M’D and MC. P P M M C C V C V N N 0° 257 N N N A A O B B 0° 257 O D D M M
  35. 35. Join points M and M’ to N and N’ and draw arcswith centres M’ and M and with radius M’D and MC. P P M M C C V C V N N 0° 257 257 0° N N N A A O B B 0° 257 O D D M M
  36. 36. Join points M and M’ to N and N’ and draw arcswith centres M’ and M and with radius M’D and MC. P P M M C C V C V 257 0° N N 0° 257 257 0° N N N A A O B B 0° 257 O D D M M
  37. 37. Join points M and M’ to N and N’ and draw arcswith centres M’ and M and with radius M’D and MC. P P M M C C V C V 257 0° N N 0° 257 257 0° N N N A A O B B 0° 257 O D D M M
  38. 38. Finally, draw arcs with centres N and N’ and radius NA and N’B. P M C V N N A O B D M
  39. 39. Finally, draw arcs with centres N and N’ and radius NA and N’B. 0° P 95 M C V N N A O B D M
  40. 40. Finally, draw arcs with centres N and N’ and radius NA and N’B. 0° P 95 M 0° 95 C V N N A O B D M
  41. 41. Finally, draw arcs with centres N and N’ and radius NA and N’B. 0° P 0° 95 M 0° 95 95 C V N N A O B D M
  42. 42. Finally, draw arcs with centres N and N’ and radius NA and N’B. 0° P 0° 95 M 0° 95 95 C V N N A O B D M
  43. 43. Finally, draw arcs with centres N and N’ and radius NA and N’B. 0° P 0° 95 M 0° 0° 95 9595 C V N N A O B D M
  44. 44. Finally, draw arcs with centres N and N’ and radius NA and N’B. 0° P 0° 95 M 0° 0° 95 9595 C V N N A O B D M
  45. 45. Draw an ovoid knowing that the lenght of its minor axis is AB
  46. 46. Get point O by drawing the perpendicular bisector of the known axis AB. A B
  47. 47. Get point O by drawing the perpendicular bisector of the known axis AB. 0° 0 A B
  48. 48. Get point O by drawing the perpendicular bisector of the known axis AB. 0° 104 A B
  49. 49. Get point O by drawing the perpendicular bisector of the known axis AB. 0° B 104 A
  50. 50. Get point O by drawing the perpendicular bisector of the known axis AB. 0° 104 A B
  51. 51. Get point O by drawing the perpendicular bisector of the known axis AB. 0° 104 A B
  52. 52. Get point O by drawing the perpendicular bisector of the known axis AB. A B
  53. 53. Get point O by drawing the perpendicular bisector of the known axis AB. A B
  54. 54. Get point O by drawing the perpendicular bisector of the known axis AB. A B O
  55. 55. Get point O by drawing the perpendicular bisector of the known axis AB. A B O
  56. 56. With its centre at O and radius OA, draw acircumference that intersects the perpendicular bisector at point P. A B O
  57. 57. With its centre at O and radius OA, draw acircumference that intersects the perpendicular bisector at point P. 0° 86 A B O
  58. 58. With its centre at O and radius OA, draw acircumference that intersects the perpendicular bisector at point P. 0° 86 A B O
  59. 59. With its centre at O and radius OA, draw acircumference that intersects the perpendicular bisector at point P. A B O
  60. 60. With its centre at O and radius OA, draw acircumference that intersects the perpendicular bisector at point P. A B O P
  61. 61. Join points A and B to P to give us the lines r and s. A B O P
  62. 62. Join points A and B to P to give us the lines r and s. A B O P
  63. 63. Join points A and B to P to give us the lines r and s. A B A O B O P P
  64. 64. Join points A and B to P to give us the lines r and s. A B A O B O P P r s
  65. 65. Draw two arcs with radius AB and centres at points A and B to get the points M and M’. A B O P r s
  66. 66. Draw two arcs with radius AB and centres at points A and B to get the points M and M’. 0° 172 AA BB O O PP rr ss
  67. 67. Draw two arcs with radius AB and centres at points A and B to get the points M and M’. 0° 172 AA BB O O PP rr ss
  68. 68. Draw two arcs with radius AB and centres at points A and B to get the points M and M’. 0° 0° 172 172 AA BB O O PP rr ss
  69. 69. Draw two arcs with radius AB and centres at points A and B to get the points M and M’. 0° 0° 172 172 AA BB O O PP rr ss
  70. 70. Draw two arcs with radius AB and centres at points A and B to get the points M and M’. 0° 0° 172 172 AA BB O O PP rr ss
  71. 71. Draw two arcs with radius AB and centres at points A and B to get the points M and M’. 0° 0° 172 172 AA BB O O PP rr ss
  72. 72. Draw two arcs with radius AB and centres at points A and B to get the points M and M’. 0° 0° 172 172 AA BB O O PP M M rr ss
  73. 73. With P as its centre and radius PM or PM’, draw the last arc to finish our ovoid. A B O P M M r s
  74. 74. With P as its centre and radius PM or PM’, draw the last arc to finish our ovoid. 0° 0 AA BB OO PP M M M M rr ss
  75. 75. With P as its centre and radius PM or PM’, draw the last arc to finish our ovoid. 0° 0 0° 53 AA BB OO PP M M M M rr ss
  76. 76. With P as its centre and radius PM or PM’, draw the last arc to finish our ovoid. 0° 0 0° 53 AA BB OO PP M M M M rr ss 53 0°
  77. 77. With P as its centre and radius PM or PM’, draw the last arc to finish our ovoid. 0° 0 0° 53 AA BB OO PP M M M M rr ss 53 0°
  78. 78. With P as its centre and radius PM or PM’, draw the last arc to finish our ovoid. 0° 0 0° 53 AA BB O O PP M M M M rr ss 53 0°
  79. 79. Draw a spiral withcentres O and O’
  80. 80. Draw a straight line and define two points on it, O and O’. O O
  81. 81. With point O as your centre, and using a radius ofthe segment OO’, draw a semi circle (which will give us point A at its intersection with the straight line). O O 0 0°
  82. 82. With point O as your centre, and using a radius ofthe segment OO’, draw a semi circle (which will give us point A at its intersection with the straight line). O O 86 0°
  83. 83. With point O as your centre, and using a radius ofthe segment OO’, draw a semi circle (which will give us point A at its intersection with the straight line). 0° 86 O O
  84. 84. With point O as your centre, and using a radius ofthe segment OO’, draw a semi circle (which will give us point A at its intersection with the straight line). O O
  85. 85. With point O as your centre, and using a radius ofthe segment OO’, draw a semi circle (which will give us point A at its intersection with the straight line). A O O
  86. 86. Using point O’ as the centre and radius O’A, drawanother semi circle to get point B on the straight line. A O O
  87. 87. Using point O’ as the centre and radius O’A, drawanother semi circle to get point B on the straight line. 0° 0 A O O
  88. 88. Using point O’ as the centre and radius O’A, drawanother semi circle to get point B on the straight line. 0° 172 A O O
  89. 89. Using point O’ as the centre and radius O’A, drawanother semi circle to get point B on the straight line. A O O 172 0°
  90. 90. Using point O’ as the centre and radius O’A, drawanother semi circle to get point B on the straight line. A O O B
  91. 91. Draw another semi circle using O as its centre andwith a radius OB to get point C on the straight line. And so, in this way, we will get our spiral. A O O B
  92. 92. Draw another semi circle using O as its centre andwith a radius OB to get point C on the straight line. And so, in this way, we will get our spiral. A O O B 257 0°
  93. 93. Draw another semi circle using O as its centre andwith a radius OB to get point C on the straight line. And so, in this way, we will get our spiral. 0° 257 A O O B
  94. 94. Draw another semi circle using O as its centre andwith a radius OB to get point C on the straight line. And so, in this way, we will get our spiral. A O O B
  95. 95. Draw another semi circle using O as its centre andwith a radius OB to get point C on the straight line. And so, in this way, we will get our spiral. C A O O B
  96. 96. Draw a spiral withcentres on the vertices of the equilateral triangle
  97. 97. Draw an equilateral, extend its sides and number its vertices: 1, 2 and 3. 1 3 2
  98. 98. Draw an equilateral, extend its sides and number its vertices: 1, 2 and 3. 1 3 2
  99. 99. With radius 1-3 and its centre at point 1, draw an arcuntil we define point A on the extension of side 2-1 of the triangle. 1 3 2
  100. 100. With radius 1-3 and its centre at point 1, draw an arcuntil we define point A on the extension of side 2-1 of the triangle. 0° 0 1 3 2
  101. 101. With radius 1-3 and its centre at point 1, draw an arcuntil we define point A on the extension of side 2-1 of the triangle. 0° 81 1 3 2
  102. 102. With radius 1-3 and its centre at point 1, draw an arcuntil we define point A on the extension of side 2-1 of the triangle. 0° 81 1 3 2
  103. 103. With radius 1-3 and its centre at point 1, draw an arcuntil we define point A on the extension of side 2-1 of the triangle. 1 3 2
  104. 104. With radius 1-3 and its centre at point 1, draw an arcuntil we define point A on the extension of side 2-1 of the triangle. A 1 3 2
  105. 105. Repeat this process with radius 2A and the centre at point 2 (making an arc that give us point B on the extension of side 3-2 of the triangle). A 1 3 2
  106. 106. Repeat this process with radius 2A and the centre at point 2 (making an arc that give us point B on the extension of side 3-2 of the triangle). A 0° 0 1 3 2
  107. 107. Repeat this process with radius 2A and the centre at point 2 (making an arc that give us point B on the extension of side 3-2 of the triangle). A 1 3 2 164 0°
  108. 108. Repeat this process with radius 2A and the centre at point 2 (making an arc that give us point B on the extension of side 3-2 of the triangle). A 1 3 2
  109. 109. Repeat this process with radius 2A and the centre at point 2 (making an arc that give us point B on the extension of side 3-2 of the triangle). A 1 3 B 2
  110. 110. Alternate this procedure successively (centre at 3and radius 3B to define point C, etc.) to draw out the spiral. A 1 3 B 2
  111. 111. Alternate this procedure successively (centre at 3and radius 3B to define point C, etc.) to draw out the spiral. A 1 3 B 2 0 0°
  112. 112. Alternate this procedure successively (centre at 3and radius 3B to define point C, etc.) to draw out the spiral. A 1 3 B 2 249 0°
  113. 113. Alternate this procedure successively (centre at 3and radius 3B to define point C, etc.) to draw out the spiral. A 1 3 B 2 0° 249
  114. 114. Alternate this procedure successively (centre at 3and radius 3B to define point C, etc.) to draw out the spiral. A 1 3 B 2
  115. 115. Alternate this procedure successively (centre at 3and radius 3B to define point C, etc.) to draw out the spiral. A 1 3 B 2 C
  116. 116. Constructing ovals,ovoids and spirals

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