Knowledge

Seven circles theorem

Source 📝

20: 123: 150: 221: 55:. Though elementary in nature, this theorem was not discovered until 1974 (by Evelyn, Money-Coutts, and Tyrrell). 19: 201: 64: 51:
drawn between opposite pairs of the points of tangency on the seventh circle all pass through the same
195: 102: 94: 142: 135: 168: 146: 119: 86: 52: 48: 40: 171: 215: 106: 205: 16:
A chain of six circles tangent to a seventh circle and each to its 2 neighbors
176: 28: 98: 44: 185: 47:
to a seventh circle and each tangent to its two neighbors, the three
36: 189: 90: 188:
by Michael Borcherds showing The Seven Circles Theorem made using
114:
Evelyn, C. J. A.; Money-Coutts, G. B.; Tyrrell, J. A. (1974).
198:
by Stanley Rabinowitz, with a proof based on Ceva's theorems.
137:
The Penguin Dictionary of Curious and Interesting Geometry
77:
Cundy, H. Martyn (1978). "The seven-circles theorem".
134: 43:. Specifically, given a chain of six circles all 35:is a theorem about a certain arrangement of seven 116:The Seven Circles Theorem and Other New Theorems 8: 18: 7: 141:. New York: Penguin Books. pp.  14: 118:. London: Stacey International. 1: 238: 196:the Seven Circles Theorem 79:The Mathematical Gazette 172:"Seven Circles Theorem" 222:Theorems about circles 24: 202:Seven Circles Theorem 33:seven circles theorem 23:Seven circles theorem 22: 65:Brianchon's theorem 186:Interactive Applet 169:Weisstein, Eric W. 133:Wells, D. (1991). 25: 125:978-0-9503304-0-2 229: 182: 181: 156: 140: 129: 110: 85:(421): 200–203. 237: 236: 232: 231: 230: 228: 227: 226: 212: 211: 167: 166: 163: 153: 132: 126: 113: 91:10.2307/3616692 76: 73: 61: 41:Euclidean plane 17: 12: 11: 5: 235: 233: 225: 224: 214: 213: 210: 209: 199: 193: 183: 162: 161:External links 159: 158: 157: 151: 130: 124: 111: 72: 69: 68: 67: 60: 57: 15: 13: 10: 9: 6: 4: 3: 2: 234: 223: 220: 219: 217: 207: 203: 200: 197: 194: 191: 187: 184: 179: 178: 173: 170: 165: 164: 160: 154: 152:0-14-011813-6 148: 144: 139: 138: 131: 127: 121: 117: 112: 108: 104: 100: 96: 92: 88: 84: 80: 75: 74: 70: 66: 63: 62: 58: 56: 54: 50: 46: 42: 38: 34: 30: 21: 206:Cut-the-knot 175: 136: 115: 82: 78: 32: 26: 71:References 177:MathWorld 107:250436639 216:Category 190:GeoGebra 59:See also 29:geometry 143:227–228 99:3616692 45:tangent 39:in the 37:circles 149:  122:  105:  97:  31:, the 103:S2CID 95:JSTOR 53:point 49:lines 147:ISBN 120:ISBN 204:at 87:doi 27:In 218:: 174:. 145:. 101:. 93:. 83:62 81:. 208:. 192:. 180:. 155:. 128:. 109:. 89::

Index


geometry
circles
Euclidean plane
tangent
lines
point
Brianchon's theorem
doi
10.2307/3616692
JSTOR
3616692
S2CID
250436639
ISBN
978-0-9503304-0-2
The Penguin Dictionary of Curious and Interesting Geometry
227–228
ISBN
0-14-011813-6
Weisstein, Eric W.
"Seven Circles Theorem"
MathWorld
Interactive Applet
GeoGebra
the Seven Circles Theorem
Seven Circles Theorem
Cut-the-knot
Category
Theorems about circles

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.