CPhill

It has been shown that, utilizing Euclidean geometry, a circle cannot be squared using a compass and a straightedge.

However, certain curves can be "squared" utilizing certain constructions.....here is one....the lune

In the unit circle CBD above, constuct semicircle CGB with radius FB = (1/2)√2

Then the area of this half circle = (1/2)*pi*(1/2)√2)^2 = pi/4

And the area of the sector ACB in the large circle = pi/4

And subtracting the common area of both of the above - the area bounded by segment CB and minor arc CB - we have that the area of the lune CGB = the area of the triangle ACB

Therefore, 4 times the area of this lune would equal the area of an inscribed square in the larger circle.....in effect, we have "squared" areas bounded by curves....!!!

BJ's correct, Z-man  !!!

d = √[S^2 + S^2 + S^2] = √[3S^2] = S√3

b = √[S^2 + S^2] = √[2S^2] =  S√2

So.... d - b = S(√3 - √2) = about .318(S)

I just thought of it.....silly me !!!

Thx, anyway, BJ..!!!

I love pie

I love cake

Give me more

For goodness sake  !!!!

A dessert often accompanied by milk or coffee.............favorite types are cherry, apple, pecan, peach, pumpkin and, occasionally,..... humble........

10m / 3sec =

200m / 1 min =

12000m / 1 hr =

12km/ hr

{That's some pretty fast walking  !!}

Let her father's age be = x      so we have

(3/8)x - 2  = 13   add 2 from both sides

(3/8)x = 15     multiply both sides by 8/3

x = 15(8/3)  = 40   = her father's age

x²-21.75x=-15.75   multipy through by 100 to clear the decimals

100x^2 - 2175x = -1575    add 1575 to both sides

100x^2 - 2175x +`1575 = 0    divide by 25

4x^2 - 87x + 63 = 0   factor

(4x - 3)(x - 21) = 0    and setting each factor to 0, we have that x = 3/4 or x = 21

Let's find the radius, first....this is given by √[(10-4)^2 + (11-6)^2 ] = √[36 + 25] = √61

So we have

(x - h)^2 + (y - k)^2 = r^2       where (h, k) is the center

(x - 4)^2 + (y - 6)^2  = 61