[HM] Quadrature of the circle
Staffan Rodhe (book@kubkou.se)
Tue, 11 May 1999 13:26:36 +0200
Dear members of the list,
Does anyone know more about the Curve y=2axx/(aa-xx). The area between the
curve (in the interval x < 0) and the y-axis is the same as the area of a
circle with radius a. The construction of the curve uses a semicircle
(radius a, x > 0) with center in (0, -a). The tangents of the semicircle at
a point (s,t) meet the x-axis in (u,0). The curve is then (x,y)=(-u,t).
I have seen (in a book by the Swedish mathematician Duhre, 1721) the
quadrature of the circle with help of a Cavalieri-Wallis-method of finding
the quadrature of the curve. There is though no references about this
special method using the curve I described.
I would be very grateful if someone could tell me more about the use of the
curve. Perhaps it has got a special name? Who else used it to find the
quadrature of the circle?
Best greetings and I hope you got the description of the curve
Staffan Rodhe