Fwd: Is 64 = 65 ???

[avinas parate]

Hi all
This is answer to Yogesh's Puzzle i.e. Is 64 = 65 ???
Well this is not true. & mathematics is not wrong. This is because of illusion.
Answer.
The first thing is As you see in the figure1 attached, in 1st square  i.e. 8x8 in upper rectangle the the slope is taken over 3x8 (pink & green) & in lower rectangle where the slope is taken on 2x5 (blue & orange)

So in Figure2 you will find that in upper rectangle, the slope that is taken over 3x8 (pink & green) which is a hypoteneous of green triangle ABC, now when you consider a triangle DBC in same big triangleABC you consider the two perpendicular sides as 2 & 5 (pink & green) which is not true. since if you therotically find the angle ABC which is arctan(3/8)= 20.55 & from this angle if you calculate the length of verticle side DE=x (which you are considering as 2 unit) of green triangle with BE=5 & angle ABC=20.55, then for triangle DBC we have, arctan(x/5)=20.55, then solving this comes out x= 1.875 =DE & not 2 so creates a gap of (2-1.875=0.125).  Now if you consider the blue/orange triangle of 2x5 in which the slope is taken over 2x5, with verticle side of 2, so this blue triangle with cut length of 2 unit is placed over a green tringle whose height is 1.875 over length of 5, in the next rectangle of 5x13 by approximating this gap of 0.125 unit without noticing you.

 

If you want to check, Do this.

Since this is small figure of say each square is with a length of say 1cm each with total length of 8cmx8cm.

Now if you increase a dimension of say length of each square of 10 cm each with total lengh of 80cmx80cm & redraw all the slope you will clearly notice the gap.

Get it

 

Avinash Parate