Al-Kashi’s theorem
$$a^2=b^2+c^2-2.b.c.cos(A)$$ $$b^2=a^2+c^2-2.a.c.cos(B)$$ $$c^2=a^2+b^2-2.a.b.cos(C)$$
Equation of a circle
Circle C with center \(\Omega(\alpha;\beta) \) and radius r:$$(x-\alpha)^2 + (y-\beta)^2 = r^2$$
Pascal’s triangle
| p | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| n=0 | 1 | ||||||||||||
| 1 | 1 | 1 | |||||||||||
| 2 | 1 | 2 | 1 | ||||||||||
| 3 | 1 | 3 | 3 | 1 | |||||||||
| 4 | 1 | 4 | 6 | 4 | 1 | ||||||||
| 5 | 1 | 5 | 10 | 10 | 5 | 1 | |||||||
| 6 | 1 | 6 | 15 | 20 | 15 | 6 | 1 | ||||||
| 7 | 1 | 7 | 21 | 35 | 35 | 21 | 7 | 1 | |||||
| 8 | 1 | 8 | 28 | 56 | 70 | 56 | 28 | 8 | 1 | ||||
| 9 | 1 | 9 | 36 | 84 | 126 | 126 | 84 | 36 | 9 | 1 | |||
| 10 | 1 | 10 | 45 | 120 | 210 | 252 | 210 | 120 | 45 | 10 | 1 | ||
| 11 | 1 | 11 | 55 | 165 | 330 | 462 | 462 | 330 | 165 | 55 | 11 | 1 | |
| 12 | 1 | 12 | 66 | 220 | 495 | 792 | 924 | 792 | 495 | 220 | 66 | 12 | 1 |