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Miloslav Ciz 2024-06-20 22:01:36 +02:00
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triangle.md
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@ -32,11 +32,11 @@ Some basic facts, features and equations regarding triangles are following (bewa
- **[area](area.md)**:
- general triangle: *a * altitude(a) / 2*
- right triangle: *a * b / 2*
- **[Pythagorean theorem](pythagorean_theorem.md)**: For the lengths of the sides of a RIGHT triangle it always holds that *a^2 + b^2 = c^2*. This is extremely important and can be used to determine unknown side lengths of right triangles.
- **[Pythagorean theorem](pythagorean_theorem.md)**: For the lengths of the sides of a RIGHT triangle (i.e. one angle is 90 degrees) it always holds that *a^2 + b^2 = c^2*. This is extremely important and can be used to determine unknown side lengths of right triangles.
- **[Thales's theorem](thales_theorem.md)**: if points *A*, *B* and *C* lie on a [circle](circle.md), then they form a right triangle with hypotenuse equal to the circle diameter (and the center of the circle lying in the middle of the hypotenuse).
- **Triangle inequality**: Sum of any two side lengths can't be greater than the length of the third side, i.e. *a + b <= c*. That means that e.g. a triangle with side lengths 1, 2 and 4 can't exist because 1 + 4 > 2. If one side of a triangle is exactly the sum of the other two, the triangle is called **degenerate**, its vertices lie on the same line and it is completely "squashed".
- **Law of sines**: *a / sin(alpha) = b / sin(beta) = c / sin(gamma)*
- **Law of cosines**: Generalization of Pythagorean theorem: *a^2 = b^2 + c^2 - 2 * b * c * cos(alpha)*.
- **Law of cosines** (generalization of Pythagorean theorem to any triangle, not just right one): *a^2 = b^2 + c^2 - 2 * b * c * cos(alpha)*.
- Triangle [tessellation](tessellation.md) is one of only three possible regular plane tilings (the other two being [square](square.md) and [hexagon](hexagon.md)).
- Every triangle has two special associated [circles](circle.md):
- **[incircle](incircle.md)**: circle inside the triangle which touches each of its sides at one point, its center (incenter) lies on the intersection of all angle bisectors.