The development characteristics of ancient Indian mathematics mainly include the following points:
1. Symbol system: The ancient Indians used decimal notation to invent the number symbol of 0-9, which is now Arabic numerals. The application of this digital symbol greatly simplifies the operation of numbers and makes the counting method clearer.
2. Elementary Algebra Thought: Elementary Algebra Thought has appeared in ancient Indian mathematics, and it began to transition to pure mathematics.
3. Trigonometry: Ancient Indians made great contributions to trigonometry, which was a by-product of their keen interest in studying astronomy. In their calculation, three quantities are used-one is equivalent to modern sine, the other is equivalent to modern cosine, and the other is called "positive vector", which is numerically equal to 1-cosα. This triangulation is no longer used. They also know some relationships between trigonometric quantities, such as "the sum of squares of sine and cosine at the same angle is equal to 1" and so on.
4. The concept of irrational number: The ancient Indians accepted the concept of irrational number and applied the calculation methods and steps suitable for rational number to irrational number in practical calculation.
The development characteristics of ancient Babylonian mathematics mainly include the following points:
1.60 decimal system: Babylonian mathematics adopts the 60 decimal system, which has great advantages in calculation, such as making the expression of fractions easier.
2. Geometry: Ancient Babylonian mathematics made some progress in geometry, such as plane geometry and spherical geometry.
3. Number theory: ancient Babylonian mathematics involves some problems of number theory, such as integer decomposition and factor decomposition.
Generally speaking, ancient Indian mathematics paid more attention to the development of theory and the cultivation of mathematical thinking, while ancient Babylonian mathematics paid more attention to practicality and the application of calculation skills.