Arithmetically, the Arabs adopted and improved India's numerical notation and carry notation, and also adopted India's irrational number operation, but gave up the negative number operation. The name algebra was invented by Arabs. Arabs have also solved some linear, quadratic or even cubic equations and explained their solutions with geometric figures. For example, for the equation x2+ 10x=39, their geometric solution is as follows: make a square, assuming its side length is unknown, and then make a rectangle with x= and four sides facing outwards. Expand the whole graph into a square with a side length of x+5. The area of the whole big square is equal to the sum of the area of a square with a side length of x and the areas of four squares with a side length of x and four rectangles with a side length of x and x respectively. So the area of a big square is x2+4x times 5/2x+4 times 5/2, which is x2+ 10x+25. Because x2+ 10x=39, the area of a big square is equal to 39+25, which is 64. Therefore, the side length of a big square is equal to 8, and X is 8-2=3. Arabs also use the intersection of conic curves to solve cubic equations, which is a great progress.
The Arabs also got a more accurate pi, 2π = 6.283185307195865, and π was calculated to 17. In addition, they also introduced the tangent and cotangent of triangles, and proved the sine law of planar triangles. They also put forward a relatively complete theory of plane triangle and spherical triangle.
As a "digital bridge", Arabic mathematics also lies in translating and writing a large number of digital documents. After these works spread to Europe, numbers entered a new period of development.