Pythagoras

Definition

Pythagoras was an ancient Greek mathematician and philosopher who is best known for the Pythagorean theorem, a fundamental principle in geometry. His work has significant implications in various fields of mathematics, including algebra and trigonometry.

5 Must Know Facts For Your Next Test

1. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: $a^2 + b^2 = c^2$.
2. Pythagoras and his followers, the Pythagoreans, contributed to the development of number theory and mathematical rigor.
3. The concept of irrational numbers was discovered by Pythagoreans when they found that $\sqrt{2}$ could not be expressed as a fraction.
4. In trigonometry, Pythagorean identities such as $\sin^2(\theta) + \cos^2(\theta) = 1$ are derived from the Pythagorean theorem.
5. Pythagoras' work influences modern applications involving polar coordinates and complex numbers.

Review Questions

• What does the Pythagorean theorem state about the sides of a right-angled triangle?
• How is the concept of irrational numbers connected to Pythagoras?
• What is one example of a Pythagorean identity used in trigonometry?

Related terms

Pythagorean Theorem:

A fundamental relation in Euclidean geometry among the three sides of a right-angled triangle: $a^2 + b^2 = c^2$.

Irrational Numbers: Numbers that cannot be expressed as a ratio of two integers; their decimal expansions are non-repeating and non-terminating.

$\sin$ and $\cos$ Functions: Trigonometric functions defining relationships between angles and side lengths in right triangles; central to solving problems using polar coordinates.