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An imaginary infinite geometric tree |
2011-02-18 |
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From Elise:
An imaginary infinite geometric tree grows 1m the first day.
2nd day 2 branches and right angles to each other and each 0.5 m long.
3rd day two new branches at ends of each of previous days' 2 branches, again at right angles, and only .25m long each.
And so on, infinitely.
Q: Use relationships of right-angled triangles and high school level knowledge of geometric series to show
the tree height is limited to (4 + sqrt2)/3 m and width to (2(sqrt2 + 1))/3 m.
Answered by Robert Dawson. |
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