As shown in Figure 13, take the hypotenuse of the isosceles triangle AOB as the right edge to make two isosceles right triangles aba1 outwards. Then take the hypotenuse of the isosceles right triangle aba1 as the right edge to make the third isosceles right triangle a1bb1 outwards. If OA = ob = 1, then the area of N isosceles triangle Sn =?

As shown in Figure 13, take the hypotenuse of the isosceles triangle AOB as the right edge to make two isosceles right triangles aba1 outwards. Then take the hypotenuse of the isosceles right triangle aba1 as the right edge to make the third isosceles right triangle a1bb1 outwards. If OA = ob = 1, then the area of N isosceles triangle Sn =?

The first area is 1 * 1 / 2 = 1 / 2
The second 1 / 2 * 2 = 1
Three 1 * 2 = 2
N 2^(N-2)

As shown in the figure, it is a part of Pythagorean tree. On a square, take the side of the square as the side length to construct a right triangle, and then take the right side as the side length to make a square, and repeat the same process continuously. Let the largest side length of the square in the figure be 5, and the sum of the areas of squares a, B, C, D, e be s, and find the value of S

∵ the side length of the largest square e is 5, ∵ the area of square e = 52 = 25. According to the Pythagorean theorem, the sum of the areas of squares a, B, C, D and E is s, which is equal to the area of square e, ∵ s = 25

The square with side length of 2 cuts off four corners (four isosceles right triangles) and becomes an octagon which becomes equal. Find the side length of the octagon
Solving quadratic equation with one variable

2（√2-1）
Let the side length of an octagon be x, and choose any side
The solution of √ 2 (2-x) = 2x is: x = 2 (√ 2-1)
Or Pythagorean theorem: [(2-x) / 2] & sup2; + [(2-x) / 2] & sup2; = x & sup2;
The solution is: x = 2 (√ 2-1)
PS: √ 2 is the root 2

If the length of the side of the small square is 1,
What is the length of the right angle side of the triangle

√2 /2
The side length of the small square is the hypotenuse of the truncated isosceles right triangle, the hypotenuse is 1, and the waist circumference is 1 / √ 2 = √ 2 / 2