Two thirds as a defined mber (proof mbers exists)

Perimeter of trapeze base plus sides. We must the length of the missing side.
Base of trapeze B = 81 cm is the largest side.
Side length 1 = 15 cm is one side.
Side length 2 = 15 cm is the other side.
The inner angles of the outer pointy things is fourty-five degrees.
x is the length of the missing side.
What is the length of the missing side in centimeters?
15 + 15 + 81 = perimeter measured
111 = perimeter measured

remembered formula for trapezes
B(L+h)/2 = area (wrong!)
where h is the heigth of the trapeze

(x+B)*h/2 = area

2(15)cos(45)+(-81 cm) = x

[30cos(45) - 81 ]cm = x

calculate cosinus of 45 degrees.
a=b
a*a + b*b = c*c
calculating formula
1*1 + 1*1 = 2
2*2 + 2*2 = 8
3*3 + 3*3 = 18
4*4 + 4*4 = 32

Using the above equations we find
(c*c - b*b)/a = b
since a=b
c*c/a - a = a

Length*Length = Area for a rectangle

Length*Length/2 = Area for a triangle with a ninety degree angle
a*b/2 = Area of the triangle with two fourty-five degree angle
calculating area
1*1/2 = 1/2
2*2/2 = 2
3*3/2 = 3
4*4/2 = 8
4*4/2 = 2*2 + 2*2
a*b/2 = a*a + b*b = c*c = 8

a/c = cos(45)
b/c = cos(45)
(a/c)*(a/c) = cos(45)
a = b = c*cos(45)
a*a/(c*c) = 2*2/8 = cos(45)*cos(45)
1/2 = cos(45)*cos(45) =
n*n = [cos(45)]^2
c*c/a - a = a
n*n/a - a = a
n*n = 2a*a
n/2a = a/n
n/2a - a/n = 0

number, area and formula comparaison
n/2a - a/n  < a*a/2 < 2a*a
number < area < formula
dividing by 2a
n/4a - 1/2n < a/4 < 2a
n/4a*a - 1/2n < 1/4 < 2
n/4a*a - 1/2n - 1/4 < 0 < 3/2
I know for sure that my number n is smaller than 3/2.
-1/4 < -n/4a*a +1/2n < 3/2 -n/4a*a + 1/2n
I know for sure that my number n is greater -1/4.
I can't do anything with -1/4. I must use the other two equations.
-n/4a*a +1/2n < 3/2 - n/4a*a + 1/2n
adding n/4a*a
1/2n < 3/2 - 1/2n
I now have a better way of making guesses.
Dividing by n Multiplying by n
1/(2n*n) < 3/2 - 1/(2n*n) 1/2 < 3n/2 - 1/2
Now I know that my number is between 1/2 and 3/2!
From multiplication
0 < 3n/2 - 1
0 < 3n - 2
0 < n - 2/3
2/3 < n
I now know that my number is smaller than 2/3 and greater than 1/2.

Now I know that my number is between 1/2 and 2/3. Now I can calculate it.

1/2 + 1/x < 2/3 != n
1/2 < 2/3 - 1/x != n - 1/x

I cannot calculate it by adding or subtracting until I reach one or the other number.

I'll try it with a circle!
2*pi*r = circumferance of a circle
pi*r*r = area of a circle
It's even more complicated!

I'll make a shape with 1/2, and the formula with 2/3.

(1/2)*(1/2)/2 = area
(2/3)*(2/3) + (2/3)(2/3) = formula
1/6 = area
8/9 = formula
Since that area is a triangle, I'll add another triangle to it!
1/6 + triangle = bigger area
That first triangle was smaller than 1/2. That's weird.
1/6 + 1/6 = 1/3 = rectangle
The rectangle I made is NOT smaller than the triangle, but my area is smaller than my number!
8/9 - 1/3 = 5/9
Now why did I do this!?
My area is a number, my formula is a number, but I can't add them together!
One is a space. But which one? I think they both are. It's confusing!
I need both areas to be numbers I can add together, so they make one number.
5/9 is where they both get along. I like that.
I'll add him to the area of the triangle.
(1/2)*(1/2+5/9)/2
(1/2)*(19/2)/2
(19/2)/4
19/8
That's fun. Now I have to make it work.
I'll switch them!
(2/3)*(2/3) = Area of rectangle
4/9 = Area of rectangle
4/9 + 1 = 13/(9+1special) = Area of triangle
formula
(1/2)*(1/2) + (1/2)*(1/2) = 1/2
1/4 + 1/4 = 1/2

So this rectangle is good. I'll add a triangle to him, and point it to the number. I can do it! (i think)
The big number is on top of him. Somewhere. Hmm.

(2/3+1)*(2/3+1) = Area of special rectangle
(5/3)*(5/3) = 25/9
Reverse formula
25/9 = 12.5/4.5 + special
6.25/2.25 + other special
3.125/1.125 + new special
1.6125/0.5625 + final special
The denominator is tending towards a number, and the numerator is still above 1/2. That's good. We
work with him.
2.8666666666666666666666666666667 + final special
final special is -2.2!!!!!!
And now you have 2/3.
Done.

1.2 = 2.4/2
-1.1 = -2.2/2
adding the two numbers
0.1 = 0.02*0.05
cos(9*5)
a/c = cos(45)
a/c = sin(45)
cos(45)cos(45) + sin(45)sin(45) = (a/c)(a/c)
1/2 = 1/4 + 1/4 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8
2/3 = 1.6125/0.5625 - 2.2



n*n=h
a/c = cos(45)
a*(c*c - b*b)/2a = Area of triangle
in this case
2a*a = c*c

1/2 = Area = Length*Length/2
1/(2*Length) = (1/2)/a = (1/2)/b = Area/Length
1/(2*Length) = (1/2)/3 = 1/6
6/(2*Length) = 1
6/2 = Length

a*a/2c + b*b/2c = c/2
0.5/c + 0.5/c = c/2
1/c = c/2
0.5 = c*c
50*0.01 = c*c*100*0.01
5*10*0.01 =
5*2*5*0.01 =
2*25*0.01 =
(2*0.25) = c*c(1)

500*0.001 = c*c*1000*0.001
2*250*0.001 =
2*125*2*0.001 =
2*25*5*2*0.001 =
2*2*5*5*5*0.001 =


2*2*5*5*5*0.001 = 1/cos(45)*1/cos(45)
2*2*5*5*5*0.001 = c/cos(45)
2*2*5*5*5*0.001*cos(45) = c
a*a + b*b = 2*2*5*5*5*0.001*cos(45)*c
(a*a + b*b)/2*2*5*5*5*0.001 = c*cos(45)