Football is made of 32 pieces of black and white cowhide, in which the black leather is a regular pentagon and the white leather is a regular hexagon. If there are x pieces of white leather, there are (32-X) pieces of black leather, each white leather has 6 sides, and * * * has 6X sides. Because every piece of white leather has three sides sewn together with black leather, black leather has three sides.
3x=[32-x]*5
x=20
That is, 20 white pieces and 32-20 black pieces =12.
How many black and white squares are there in football? Speaking of football, everyone is familiar with it. Can you tell me how many black pentagons and white hexagons there are in football? Haha, you may not have counted it. All right, let's count them together. If we take six black blocks and count them again, we will find that there are still six black blocks. Then, it goes without saying that the black block is 12. There are more white blocks than black blocks. Of course, I can also use the method just now to count, or write numbers on the counted blocks to show the difference. But it doesn't seem to be without it, but we have to analyze it first: the black block is pentagonal, the white block is hexagonal, and the five sides of each black block coincide with one side of five white skins. Three sides of each white leather are sewn together with three black leather respectively. The whole football surface is closed, and the black skin and the white skin are closely connected. If the white skin has W (white), then one * * * has six white blocks, some of which are connected with the white skin. The other part is connected with black leather. Each white leather has three edges connected with the black leather, so a * * * has 3W white edges connected with the black leather. Black leather has 60 sides, so white leather is 20 pieces. Isn't it interesting? A football has 32-x pieces of leather, black and white is a regular Pentagon, and white is a regular hexagon with x pieces of black leather. Column equation: 5x+(32-x)*6=E*2 (two skins per side * *) 5x+(32-x) * 6 = v * 3 (three skins per vertex * * *) V+32-E=2 (Euler formula) and x = is obtained.
Each pentagon is connected with five hexagons.
Each hexagon is connected with three pentagons.
So the ratio of pentagon to hexagon is 3:5.
Pentagon 3x+5x=32
Pentagon 3x= 12
Hexagonal 5x=20
A regular hexagon has six sides and a regular pentagon has five sides. If a regular hexagon is x-fast, then a regular pentagon is 32-X-fast, and there are 2X sides overlapping (6-2)X=5(32-X) between the regular hexagon and the regular hexagon, and then calculate!
Football is made of 32 pieces of black and white cowhide. Black leather can be regarded as a regular Pentagon and white leather as a regular hexagon. Let the white leather have x blocks, then the black leather has (32-x) blocks, and each white leather has six sides, with ***6x sides. Every white leather has three sides connected with black leather, so black leather has only three sides. Black leather is a regular pentagon, and the number of sides of black leather is 5(32-x). Each white leather has three sides connected with black leather. ∴ Black leather * *