Eisatopon Math AI Challenges: Απόδειξη χωρίς λόγια

Σάββατο 12 Οκτωβρίου 2013

Απόδειξη χωρίς λόγια

\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \dots = \frac{1}{2}

Here is a visual proof that 1/3 + 1/9 + 1/27 + … = 1/2 (each term is a third of the one before it.) This is shown by finding red areas, each one of which is a third of the area of the one before it. To split a triangle into thirds, you can simply find the midpoint and cut from there out to the three corners. At the end of the animation, we see that we are filling in the left half of the big triangle with red, which suggests the infinite sum is equal to a half. [code] [more]

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