"Euclidea3"-eta-07

Q:

Analysis: Given the full use of the three equal points and angle of information, here we only need to make a 36° corner.

Consider a isosceles triangle with a top angle of 36°. Such as.

Set AD=A1,CD=A2, according to similar, easy to get a1:a2= (√5-1)/2.

So we just need to find an arbitrary long line segment that proportion of the split point, you can make a isosceles triangle with 36°.

The question now is how to make this split point through the ruler gauge. Look at such a diagram.

The drawing process of ruler gauge, B is the dividing point of this proportion.

Therefore, the 54° can eventually be used as the three equal angles.

Ps:

(1) The ratio is known as the golden ratio.

(2) If the previous step is not the optimal step.

"Euclidea3"-eta-07