Your SlideShare is downloading. ×
Constructing ovals, ovoids and spirals
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

Constructing ovals, ovoids and spirals

297

Published on

Published in: Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
297
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
0
Comments
0
Likes
0
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. Constructing ovals,ovoids and spirals
  • 2. Draw an oval knowing thelenght of axes AB and CD
  • 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Draw an ovoid knowing that the lenght of its minor axis is AB
  • 46. Get point O by drawing the perpendicular bisector of the known axis AB. A B
  • 47. Get point O by drawing the perpendicular bisector of the known axis AB. 0° 0 A B
  • 48. Get point O by drawing the perpendicular bisector of the known axis AB. 0° 104 A B
  • 49. Get point O by drawing the perpendicular bisector of the known axis AB. 0° B 104 A
  • 50. Get point O by drawing the perpendicular bisector of the known axis AB. 0° 104 A B
  • 51. Get point O by drawing the perpendicular bisector of the known axis AB. 0° 104 A B
  • 52. Get point O by drawing the perpendicular bisector of the known axis AB. A B
  • 53. Get point O by drawing the perpendicular bisector of the known axis AB. A B
  • 54. Get point O by drawing the perpendicular bisector of the known axis AB. A B O
  • 55. Get point O by drawing the perpendicular bisector of the known axis AB. A B O
  • 56. With its centre at O and radius OA, draw acircumference that intersects the perpendicular bisector at point P. A B O
  • 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. With its centre at O and radius OA, draw acircumference that intersects the perpendicular bisector at point P. 0° 86 A B O
  • 59. With its centre at O and radius OA, draw acircumference that intersects the perpendicular bisector at point P. A B O
  • 60. With its centre at O and radius OA, draw acircumference that intersects the perpendicular bisector at point P. A B O P
  • 61. Join points A and B to P to give us the lines r and s. A B O P
  • 62. Join points A and B to P to give us the lines r and s. A B O P
  • 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Draw a spiral withcentres O and O’
  • 80. Draw a straight line and define two points on it, O and O’. O O
  • 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Draw a spiral withcentres on the vertices of the equilateral triangle
  • 97. Draw an equilateral, extend its sides and number its vertices: 1, 2 and 3. 1 3 2
  • 98. Draw an equilateral, extend its sides and number its vertices: 1, 2 and 3. 1 3 2
  • 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Constructing ovals,ovoids and spirals

×