What were the major contributions of Ancient Greece to mathematics?

Ancient Greece made significant contributions to the field of mathematics, which laid the foundation for many mathematical concepts and principles that are still used today. Some of the major contributions of Ancient Greece to mathematics include:

1. Geometry: The Greeks, particularly Euclid, developed the principles of geometry. Euclid's book "Elements" is considered one of the most influential mathematical works of all time. It introduced the axiomatic method and provided a systematic approach to geometry, including the concepts of points, lines, angles, and shapes.

2. Pythagorean Theorem: The Pythagorean theorem, named after the Greek mathematician Pythagoras, states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem is fundamental in geometry and has numerous applications in various fields.

3. Trigonometry: Ancient Greeks, particularly Hipparchus, made significant advancements in trigonometry. They developed the concept of trigonometric functions, such as sine, cosine, and tangent, which are essential in measuring angles and distances in triangles. These concepts were further expanded upon by later mathematicians.

4. Calculating Pi: Ancient Greeks were the first to make attempts at calculating the value of pi (π), which represents the ratio of a circle's circumference to its diameter. Archimedes, in particular, made significant progress in approximating the value of pi using geometric methods.

5. Mathematical Proof: Ancient Greeks emphasized the importance of mathematical proof and logical reasoning. They developed rigorous methods of proof, which became the basis for modern mathematical proofs. Mathematicians such as Euclid and Pythagoras laid the groundwork for deductive reasoning and the use of axioms and theorems.

These contributions of Ancient Greece to mathematics not only advanced the field during their time but also provided a solid foundation for future mathematical developments.