Upcoming SlideShare
×

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.
Standard text messaging rates apply

# Constructing ovals, ovoids and spirals

297

Published on

Published in: Education
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

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

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