1, Pythagorean theorem.
The proof of Pythagorean theorem is the beginning of demonstrating geometry; Pythagorean theorem is the first theorem in history that connects number with shape, that is, the first theorem that connects geometry with algebra; Pythagorean theorem led to the discovery of irrational numbers and the first mathematical crisis, which greatly deepened people's understanding of logarithm; Pythagorean theorem is the first indefinite equation in history to give a complete solution, which leads to Fermat's last theorem.
Pythagorean theorem is the basic theorem of Euclidean geometry and has great practical value. This theorem is not only a dazzling pearl in geometry, but also widely used in advanced mathematics and other scientific fields. 1971May 15, Nicaragua issued a set of stamps entitled "Ten Mathematical Formulas for Changing the World". These ten mathematical formulas are all selected by famous mathematicians, and Pythagorean theorem is the first one.
2, round.
A circle is a closed curve formed by rotating a moving point around a certain point on a plane for a certain length. The standard equation is (x-a)? +(y-b)？ =r？ , where point (a, b) is the center of the circle and r is the radius.
A circle is a geometric figure, and it is also a figure with axial symmetry and central symmetry. At the same time, the circle is a positive infinite polygon. The more sides a polygon has, the closer its shape, perimeter and area are to a circle. Because "infinity" is a concept, there is no real circle in the world, only conceptual graphics.
3. The inside and outside angles of a triangle.
The outer angle of a triangle is the angle formed by one side of the triangle and the opposite extension line of the other side. The sum of the three outer angles of a triangle is 360 degrees. Every vertex of a triangle has two equal external angles, so every triangle has six external angles. The outer angle of a triangle is greater than any non-adjacent inner angle, and the outer angle of a triangle is equal to the sum of two non-adjacent inner angles.
Mathematically, the sum of the internal angles of a triangle is 180, and the sum of the internal angles of a quadrilateral (polygon) is 360. And so on, add an edge, and the sum of internal angles will add 180. The formula of the sum of internal angles is (n-2) × 180. The degree of each inner angle of a regular polygon is (n-2) × 180 ÷ n, for example, the sum of the inner angles of a triangle is the sum of three angles inside the triangle, and one inner angle is any one of them.