1. Constructing ovals,
ovoids and spirals

3. Draw an oval knowing the
lenght of axes AB and CD

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.
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.
0°
179
C
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.
C
179 0°
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 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

10. Draw an arc with radius CP and the centre on C
until it intersects segment AC at V.
P
C
A O B
D

11. 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

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
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 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

16. Draw its perpendicular bisector AV, wich will
intersect OD or its extension at point M, as well as
the major semiaxis at point N.
P
C
V
A O B
D

17. Draw its perpendicular bisector AV, wich will
intersect 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

18. Draw its perpendicular bisector AV, wich will
intersect 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

19. Draw its perpendicular bisector AV, wich will
intersect 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 will
intersect 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 will
intersect 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

22. Draw its perpendicular bisector AV, wich will
intersect 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 its perpendicular bisector AV, wich will
intersect 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

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
D
M

25. 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

26. 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

27. 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

28. 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

29. Join points M and M’ to N and N’ and draw arcs
with centres M’ and M and with radius M’D and MC.
P
M'
C
V
N N'
A O B
D
M

30. Join points M and M’ to N and N’ and draw arcs
with centres M’ and M and with radius M’D and MC.
P
M'
C
V
N N'
N'
A O B
D
M

31. Join points M and M’ to N and N’ and draw arcs
with 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 arcs
with 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 arcs
with centres M’ and M and with radius M’D and MC.
P
M'
C
C
V
N N'
N'
A O B
D
M

34. Join points M and M’ to N and N’ and draw arcs
with 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

35. Join points M and M’ to N and N’ and draw arcs
with 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

36. Join points M and M’ to N and N’ and draw arcs
with 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

37. Join points M and M’ to N and N’ and draw arcs
with 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. Join points M and M’ to N and N’ and draw arcs
with 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

39. 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

40. 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

41. 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

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°
95
95
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. 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

46. Draw an ovoid knowing
that the lenght of its
minor axis is AB

47. Get point O by drawing the perpendicular bisector
of the known axis AB.
A B

48. Get point O by drawing the perpendicular bisector
of the known axis AB.
0°
0
A B

49. Get point O by drawing the perpendicular bisector
of the known axis AB.
0°
104
A B

50. Get point O by drawing the perpendicular bisector
of the known axis AB.
0°
B
104
A

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.
0°
104
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

55. Get point O by drawing the perpendicular bisector
of the known axis AB.
A B
O

56. Get point O by drawing the perpendicular bisector
of the known axis AB.
A B
O

57. With its centre at O and radius OA, draw a
circumference that intersects the perpendicular
bisector at point P.
A B
O

58. With its centre at O and radius OA, draw a
circumference that intersects the perpendicular
bisector at point P.
0°
86
A B
O

59. With its centre at O and radius OA, draw a
circumference that intersects the perpendicular
bisector at point P.
0°
86
A B
O

60. With its centre at O and radius OA, draw a
circumference that intersects the perpendicular
bisector at point P.
A B
O

61. With its centre at O and radius OA, draw a
circumference that intersects the perpendicular
bisector at point P.
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
O
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

65. 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

66. 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

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°
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
rr ss

73. 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

74. 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

75. 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

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

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
OO
PP
M
M M'
M'
rr ss
53
0°

79. 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°

80. Draw a spiral with
centres O and O’

81. Draw a straight line and define two points on it, O
and O’.
O O'

82. With point O as your centre, and using a radius of
the segment OO’, draw a semi circle (which will give
us point A at its intersection with the straight line).
O O'
0
0°

83. With point O as your centre, and using a radius of
the segment OO’, draw a semi circle (which will give
us point A at its intersection with the straight line).
O O'
86
0°

84. With point O as your centre, and using a radius of
the segment OO’, draw a semi circle (which will give
us point A at its intersection with the straight line).
0°
86
O O'

85. With point O as your centre, and using a radius of
the segment OO’, draw a semi circle (which will give
us point A at its intersection with the straight line).
O O'

86. With point O as your centre, and using a radius of
the segment OO’, draw a semi circle (which will give
us point A at its intersection with the straight line).
A O O'

87. Using point O’ as the centre and radius O’A, draw
another semi circle to get point B on the straight line.
A O O'

88. Using point O’ as the centre and radius O’A, draw
another semi circle to get point B on the straight line.
0°
0
A O O'

89. Using point O’ as the centre and radius O’A, draw
another semi circle to get point B on the straight line.
0°
172
A O O'

90. Using point O’ as the centre and radius O’A, draw
another semi circle to get point B on the straight line.
A O O'
172
0°

91. Using point O’ as the centre and radius O’A, draw
another semi circle to get point B on the straight line.
A O O' B

92. Draw another semi circle using O as its centre and
with 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

93. Draw another semi circle using O as its centre and
with 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°

94. Draw another semi circle using O as its centre and
with 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

95. Draw another semi circle using O as its centre and
with 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

96. Draw another semi circle using O as its centre and
with 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

97. Draw a spiral with
centres on the vertices of
the equilateral triangle

98. Draw an equilateral, extend its sides and number its
vertices: 1, 2 and 3.
1
3
2

99. Draw an equilateral, extend its sides and number its
vertices: 1, 2 and 3.
1
3
2

100. With radius 1-3 and its centre at point 1, draw an arc
until we define point A on the extension of side 2-1 of
the triangle.
1
3
2

101. With radius 1-3 and its centre at point 1, draw an arc
until we define point A on the extension of side 2-1 of
the triangle.
0°
0
1
3
2

102. With radius 1-3 and its centre at point 1, draw an arc
until 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 arc
until we define point A on the extension of side 2-1 of
the triangle.
0°
81
1
3
2

104. With radius 1-3 and its centre at point 1, draw an arc
until we define point A on the extension of side 2-1 of
the triangle.
1
3
2

105. With radius 1-3 and its centre at point 1, draw an arc
until we define point A on the extension of side 2-1 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
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
0°
0
1
3
2

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
164
0°

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
2

110. 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

111. Alternate this procedure successively (centre at 3
and radius 3B to define point C, etc.) to draw out the
spiral.
A
1
3 B
2

112. Alternate this procedure successively (centre at 3
and radius 3B to define point C, etc.) to draw out the
spiral.
A
1
3 B
2
0
0°

113. Alternate this procedure successively (centre at 3
and radius 3B to define point C, etc.) to draw out the
spiral.
A
1
3 B
2
249
0°

114. Alternate this procedure successively (centre at 3
and radius 3B to define point C, etc.) to draw out the
spiral.
A
1
3 B
2
0°
249

115. Alternate this procedure successively (centre at 3
and radius 3B to define point C, etc.) to draw out the
spiral.
A
1
3 B
2

116. Alternate this procedure successively (centre at 3
and radius 3B to define point C, etc.) to draw out the
spiral.
A
1
3 B
2
C

117. Constructing ovals,
ovoids and spirals