Abstract
THIS is an enlarged and beautifully produced edition of a pamphlet which has been circulated before under the simpler title “The Trisection of an Angle”. Since Euclid cannot be supposed to have thought that he was giving anything but a selection of geometrical facts, it is legitimate to add to his postulates others that he did not perceive, and, in particular, to introduce the postulate that the author's construction is valid. This, of course, puts the matter beyond argument. The author relies on graphical evidence, and since his construction is in effect an identification of sin oc/(2-f cos a) with tan a, where a is one eighth of the angle to be trisected, it is not surprising that the evidence seems adequate. To do justice to the author's style, a quotation must be made: “I have the honor of introducing to the mathematical world” on another page he speaks of “students of geometry and miscellaneous circles generally”. … a new kind of Triangle … The Golden Mean Triangle will serve to show that even the scalene triangle is not to be classed among the lower host of things, ‘the loose, the lawless, the exaggerated, the insolent, and the profane’ … It can be mathematically demonstrated that the scalene triangle is capable of being invested with a certain charm and comeliness distinctly its own, by being brought into perfect relation to the GOLDEN MEAN, which lies at the heart, or at least within easy reach of every blessed one of them-whether it be lank or plump, slender or buxom, microscopic or telescopic.”
The Mathematical Atom: its Involution and Evolution exemplified in the Trisection of the Angle.
A Problem in Plane Geometry solved By Julius J. Gliebe. Third edition revised. Pp. iv + 87. (San Francisco: St. Boniface Franciscan Friary; London: Technical Records, Ltd., 1933.) 10s. 6d. net.
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N., E. The Mathematical Atom: its Involution and Evolution exemplified in the Trisection of the Angle. Nature 132, 804 (1933). https://doi.org/10.1038/132804a0
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DOI: https://doi.org/10.1038/132804a0