It can be proved that the proof of a2+b2=c2 was put forward by Liu Hui, a mathematician of Wei State in the Three Kingdoms period. In the fourth year of Wei Jingyuan (AD 263), Liu Hui annotated the ancient book Nine Chapters Arithmetic. In the annotation, he drew a diagram similar to Figure 5 (b) to prove Pythagorean theorem.
Leonardo da Vinci's proof of Pythagorean theorem is to spell out different holes with two identical pieces of paper, and the two holes have the same area. Pythagorean theorem is proved by finding that the area expressions of two holes are equal.
As shown in the figure, it is a schematic diagram of different holes spelled out by two identical pieces of paper.
The premise includes: the connecting line BE and CF intersect at G point, and the quadrilateral ABGF and quadrilateral GCDE are both squares;
Connecting B'F' and C'E', there is a quadrilateral. B'C'E'F' is a square;
Let the side length of square ABGF = a' b' = d' e' = a
The side length of a square GCDE = a' f' = c' d' = b；;
BC=EF= side length of a square B 'C 'E 'F' = c
Then the area of polygon ABCDEF = the area of square ABGF+the area of square GCDE+the area of +2×△BCG.
=a？ +b？ +2(ab÷2)=a？ +b？ +ab；
Area of polygon A'B'C'D'E'F = area of 2×△ A 'b 'f+area of square B 'c 'e 'f.
=2(ab÷2)+c？ =ab+c？ ;
And because the areas of the two holes are equal, that is, a? +b？ +ab=ab+c？ ;
So you can get an a by simplifying? +b？ =c？ , thus proving the Pythagorean theorem.
Baidu Encyclopedia-Da Vinci
Baidu Encyclopedia-Green Zhu Access Map