rpenner, You state the ratio of lengths AB:CD = 1:√3 in my diagram. I stated the above, which means the lengths of the sides are 1.772004514666935 units, not as you state "1:√3" which is 1.732050807568877 units. Care to take another stab at it?
MD, As far as anyone can tell from your diagram, it looks like you did this: Please Register or Log in to view the hidden image! Which does not give a square with sides of length 1.772 as you claim, but rather 1.732 as rpenner showed. If you are doing something different than what I show above, you need to be more clear about it, and explain your process.
Using known lengths and right triangles, work out the lengths of lines using Pythagorean theorem and find the areas. It all works out perfect to me.
In my drawing, do you see the two intersection points between the two circles? Note that the square runs exactly through those two points. Now, are you sure my drawing represents the geometry you had in mind?
In my drawing, do you see that the distance between the centers of the two circles is exactly one radius? Now, are you still sure that my drawing matches the geometry you had in mind?
Please Register or Log in to view the hidden image! In that case, you must agree that each leg of this blue equilateral triangle is one radius in length, correct?
I agree the bottom of the triangle is 1 unit in length. I say the point at the top of the triangle is \(sqrt{3.14}/2\) above the bottom line.
So you don't agree that the other two blue lines are each one radius in length? Each one is a straight line drawn from the center of a circle to the edge of that same circle. How can such a line not be one radius in length?
Not along the same axis. You trying to use smoke and mirrors on this one, Neddy? Imagine an expanding light sphere from the center point of the left circle. Does light travel along the axis that those triangle sides are, at c, from the center of the circle? No! It travels at c along the bottom line of the triangle, not the other sides.
You seriously don't recognise these blue lines as radius lines? Please Register or Log in to view the hidden image! At the bottom, I separated the circles from each other so you could see them better. Now do you see that those blue lines are radii?
Oh the joys of seeing things like synesthesians do.... I can assure you, the angles do not make sense as a hypersphere.
Along the same axis??? You are massively confused on lengths. Use my method of finding lengths of lines and areas using Pythagorean theorem, it won't fail you! Einstein will!
what units are you working with? And what is the basis for the background lines, do they radially separate positions in the sphere? In which case, I will ask the obvious, does this represent units dependent on spherical coordinates or is this a rough case of trigonometry I am unaware of?
Do you know what a Synesthesian is? We are quite rare... and mostly men. I am also a high functioning psychopath. It's funny isn't it, how people stigmatize the intelligent when they have something on them... a social agenda of stigma surrounding ill-health. But what is ill-health? And did Reiku suffer this also? As far as I am aware, my life is excellent and I seldom fail an achievement. My main interest is in psychoanalysis. What achievements have you made?
We were talking about "squaring the circle". From the wikipedia article: Please Register or Log in to view the hidden image! Squaring the circle: The areas of this square and this circle are equal. In 1882, it was proven that this figure cannot be constructed in a finite number of steps with an idealized compass and straightedge. (Bold added by me.) Contrary to the article, Motor Daddy thinks "squaring the circle" can be done in just a few steps, by using the intersection points of two circles which are one radius apart, center-to-center. He also does not realise that any straight line drawn from the center of a circle to a point on the edge of that circle is a radius, which by definition is one radius in length.
