1, Ionian mathematicians began to study mathematics by observing and explaining natural phenomena. They try to describe and predict various phenomena in nature through mathematical models, such as celestial movement and object shape. This mathematical description of natural phenomena provides important enlightenment for the later development of mathematical theory.
2. Ionian mathematicians put forward many important mathematical concepts and theorems. For example, Pythagoras put forward the famous Pythagorean theorem, that is, in a right triangle, the sum of squares of right angles is equal to the square of hypotenuse. This theorem is widely used in geometry and is still an important content in middle school mathematics.
3. Ionian mathematicians also studied important concepts such as irrational numbers and infinitesimal. They realize that some numbers can't be expressed by fractions. These numbers are called irrational numbers. At the same time, they also studied the concept of infinitesimal, that is, when a quantity is infinitely close to 0, it becomes infinitesimal. These concepts had an important influence on later calculus.
4. The achievements of Ionian mathematicians are also reflected in the improvement of mathematical symbols and expressions. They use concise symbols and expressions to describe complex mathematical problems, which makes mathematics easier to understand and apply. The improvement of this mathematical expression has also played a positive role in promoting the later development of mathematics.
The works with the highest achievements in mathematics in ancient Greece;
The Elements of Geometry is a mathematical work created by the ancient Greek mathematician Euclid, which was completed around 300 BC. It is a masterpiece of classical geometry and a symbol of the maturity of geometry.
The Elements of Geometry is divided into 13 volumes, including five kinds of 28 axioms and 465 theorems. These axioms and theorems form the basis of Euclidean geometry and make geometry a strict science. Euclid not only gave definitions and proofs in Elements of Geometry, but also established many important theorems and inferences through these definitions and proofs.
The influence of geometric elements is very profound. It not only had an important influence on ancient Greek mathematics, but also had a far-reaching influence on the later development of mathematics. It became the foundation of European mathematics and had an important influence on the development of European mathematics. At the same time, The Elements of Geometry is also one of the earliest mathematics textbooks in the world, which has had an important influence on later mathematics education.
In addition, The Elements of Geometry also has high cultural value. It is not only a mathematical work, but also a philosophical work. Euclid explored the nature and laws of the universe through geometric axioms and theorems in the Elements of Geometry, showing the pursuit of truth and the praise of human wisdom.