Can anyone square the circle with ruler and diabete?(lets see how smart you are!!)
+130560 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....!!!
+130560 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....!!!
+118725 Chris you've done a great job here and I love your pic
BUT
It never ceases to amaze me how other mathematicians answer questions that to me make absolutely no sense.
What does "square a circle" mean
What is a diabete. I looked it up - couldn't find it though.
It appears to me that either I or the anon who asked the question is not very smart.
