Applied Mathematicsematics

Great Moments in Mathematics Before 1650 (Dolciani by Howard W. Eves

By Howard W. Eves

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L . History o f Greek Mathematics. 2 vols. New York: Oxford Uni­ versity Press. 1 93 1 . HUNTLEY. H . E. The Divine Proportioll. a Study ill Mathematical Beauty. New York: Dover Publications, 1 970.

A very fruitful way of making geometrical conjectures is by the employment of analogy, though it must be confessed that many conjectures so made are ultimately proved false. An astonishing amount of space geometry has been discovered via analogy from similar situations in the plane, and in the geometry of higher dimensional spaces analogy has played a very successful role. " The pedagogical principle is that, at least in broad outline, a student should be taught a FROM THE LABORATORY INTO THE STUDY 21 subject pretty much in the order in which the subject developed over the ages.

New York: Cambridge University Press. 1 94 1 . p. 34. 47 PRECIPITATION OF THE FIRST CRISIS D A r-------� B c FIG. 1 8 central angle subtended by one side of a regular pentagon inscribed in a circle. Since, in an isosceles triangle each of whose base angles is twice the vertex angle of the triangle (see Figure 19), the base angles are 72° and the vertex angle is 36° , the problem is reduced to the construction of such an isosceles triangle. Let A C in Figure 19 bisect the base angle OAB. Then OC = AC = AB and triangle BAC is similar to triangle AOB.

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