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What are the difficulties in junior high school mathematics?
The difficulties in junior high school mathematics are Pythagorean theorem, the inner and outer angles of circles and triangles.

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.