1. Whiteboardmaths.com
© 2004 All rights reserved 5 7 2 1

2. A n i m a t e d
C u r v e
S t i t c h i n g

3. Black 5
Curve
Stitching

4. Demo 1
2 Parabolas

5. Demo 2
8 Parabolas

6. Demo 3
4 Parabolas

7. Demo 4
8 Parabolas

8. Rose Demo
How many lines?
Sum (1 to 17)
(17 x 18)/2 = 153

9. The Epicycloids is the name given to the family of curves that are traced out by the path of a point on the circumference of a circle, that rolls around the outside of a fixed circle of different radii.
Epicycloids r 2r r r
Cardioid(Single Cusp) (Heart Shaped)
Nephroid (Double Cusp) (Kidney Shaped) 3r
Epicycloid of Cremona named after the mathematician

10. Cardiod Cardioid Moving Cardioid
A Cardiod is the name given to the curve that is traced out by the path of a point on the circumference of a circle that rolls around the outside of a fixed circle of equal radius.
Cardiod
Cardioid Moving
Cardioid r r
Fixed Circle

11. Nephroid Moving Nephroid Nephroid
A Nephroid is the name given to the curve that is traced out by the path of a point on the circumference of a circle that rolls around the outside of a fixed circle of twice its radius.
Nephroid Moving
Nephroid r 2r
Fixed Circle
Nephroid

12. Epicycloid Moving Epycycloid Epicycloid of Cremona
The Epicycloid of Cremona is the name given to the curve that is traced out by the path of a point on the circumference of a circle that rolls around the outside of a fixed circle of 3 times its radius.
Epicycloid Moving
Epycycloid r 3r
Fixed Circle
Epicycloid of Cremona

13. Cardioid
n  2n
Cardioid Auto
Single
Cusp

14. Cardioid Demo n  2n Cardioid Single Cusp 72 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71
144 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
Cardioid
n  2n
Cardioid Demo
Single Cusp

15. Nephroid
n  3n
Nephroid Auto
Double Cusp

16. Nephroid Demo n  3n Nephroid Double Cusp 72 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71
144 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
Nephroid
n  3n
Nephroid Demo
Double Cusp

17. Epicycloid of Cremona
n  4n
Epicycloid Auto
Triple Cusp

18. Epicycloid Demo n  4n Epicycloid of Cremona Triple Cusp 72 1 2 3 4 56 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71
144 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
Epicycloid of Cremona
n  4n
Epicycloid Demo
Triple Cusp

19. Black 1
2 Parabolas

20. Black 2
8 Parabolas

21. Black3
4 Parabolas

22. Black4
8 Parabolas

23. Black 5
18 Point Mystic Rose

24. Static1

25. Static 2

26. Static3

27. Static 4

28. Static 5

29. Static 6

30. Cardioid
n  2n
Static 7

31. Nephroid
n  3n
Static 8

32. Epicycloid of Cremona
n  4n
Static 9

33. Worksheets

39. 72 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71
144 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143