I can figure out the short formula many contestant used and in TT(tutorial). Can anyone give me some explanation on this.. sketch etc. Thanks in Advance.
# | User | Rating |
---|---|---|
1 | ecnerwala | 3648 |
2 | Benq | 3580 |
3 | orzdevinwang | 3570 |
4 | cnnfls_csy | 3569 |
5 | Geothermal | 3568 |
6 | tourist | 3565 |
7 | maroonrk | 3530 |
8 | Radewoosh | 3520 |
9 | Um_nik | 3481 |
10 | jiangly | 3467 |
# | User | Contrib. |
---|---|---|
1 | maomao90 | 174 |
2 | awoo | 164 |
3 | adamant | 163 |
4 | TheScrasse | 159 |
4 | nor | 159 |
6 | maroonrk | 156 |
7 | -is-this-fft- | 150 |
8 | SecondThread | 147 |
9 | orz | 146 |
10 | pajenegod | 145 |
I can figure out the short formula many contestant used and in TT(tutorial). Can anyone give me some explanation on this.. sketch etc. Thanks in Advance.
Name |
---|
Extend the sides of the hexagon to form an equilateral triangle (try to see why it is an equilateral triangle). Then the area of this triangle is
sqrt(3)/4 * a^2
wherea = a1 + a2 + a3
is the length of the side of the big triangle. Notice that the area of the original hexagon equals to theArea of big triangle - Area of 3 triangles
==> thearea = sqrt(3)/4 * a^2 - sqrt(3)/4 * a1^2 - sqrt(3)/4 * a3^2 - sqrt(3)/4 * a5^2
. wherea1, a3, and a5
are the sides of the 3 triangles we added to the hexagon to form the big triangle.Now to see how many triangles of side = 1 exists we divide the area of the hexagon by the area of an equilateral triangle of side length = 1 (which equals
sqrt(3)/4
) ==> the answer =a^2 - a1^2 - a3^2 - a5^2
.