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NAIC DISSECTION QUADRATURE 5. Here is an algebraic version of Lconardos quadrature: (a) Begin with a square of side 2r and upon each side construct a semicircle. Simultancously circumscribe a circle about the square (as shown). Find the combined arca of the four semicircles in terms of r 21 2r(b) Now find the area of the circumscribed circle in terms of r. Notice anything? (c) According to (a) and (b), we get the same area if we remove the circumscribed circle from the figure above as we get if we instead remove the four semicircles from the figure above. Use this to explain why a single lune from the picture is quadrable. SQUARING THE CIRCLE? 6. Trace through the (fallacious) argument attributed to Hippocrates to the effect that the quadrature of the lune implies the quadrature of the circle (Journey Through Genius, pp. 20- 22). Be sure you can identify where the error occurs. Does anyone seriously believe this would have deceived the great Hippocrates? DENTAL NUMBERS-PART ONE (MORE LATER

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