Infinite bisections required for trisection of an angle

sum_series_1by2_equal_1by3

Figure 1: Self-evident demonstration of \frac{1}{3}=\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}...

serial_trisection

Figure 2: Application of the same as serial bisections to trisect the angle. In the example chosen here we have \theta=102^o; \; \frac{\theta}{3}=34^o. In ten steps we get to 33.97^o which is a pretty close, though in principle it shows that with a compass and straight-edge we would need infinite steps.

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