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## Thales’ Theorem – Explanation and Examples

Thales’ theorem tells us that the diameter of a circle always forms a right triangle when we connect it to any point located on the circumference of the circle. This theorem can be proved by using two isosceles triangles inscribed in a circle and using their angles....

## Problems with Thales’ Theorem

Thales’ theorem is a special case of the inscribed angles theorem. This theorem says that if we have a triangle inscribed in a circle with the diameter as the hypotenuse, the triangle will be a right triangle and will form a right angle at the vertex located at any...

## 3D Pythagorean Theorem – Formula and Examples

The 3D Pythagorean theorem is an extension of the 2D Pythagorean theorem that can be used to solve problems in three dimensions such as cubes, and rectangular pyramids. In three dimensions, the general formula of the 3D Pythagorean theorem is , where x, y, and z are...

## Properties of Pascal’s Triangle

Pascal’s triangle is a type of number pattern. The numbers are arranged in a way that reflects a triangle. First, the 1 is placed at the top. Then, the rest of the numbers are arranged in a triangular pattern. The numbers we get in each step are the sum of the two...

## Applications of Pascal’s Triangle

Pascal’s triangle has many applications in mathematics and statistics. We can use Pascal’s triangle to find the binomial expansion. Also, Pascal’s triangle is used in probabilistic applications and in the calculation of combinations. Recall that Pascal’s triangle is a...