Divide an equilateral triangle into a number of triangles that are similar to the original triangle (ie similar in shape but possibly different size and possibly rotated) so that they lie in k rows in the original triangle. If you select k = 2, 4, 8 you get the following figures (for eg k = 6 you remove the two bottom rows in the right figure, for k = 3 you delete the bottom row in the middle figure, etc.). Let ak be the number of triangles when you have k rows and consider the case k 2n, n ≥ 0. S A. Determine the values for a2m where n = 1, 2, 3, and 4. B. Using the results in task A, determine a recurrence relation for a2n, where n ≥ 0.
Divide an equilateral triangle into a number of triangles that are similar to the original triangle (ie similar in shape but possibly different size and possibly rotated) so that they lie in k rows in the original triangle. If you select k = 2, 4, 8 you get the following figures (for eg k = 6 you remove the two bottom rows in the right figure, for k = 3 you delete the bottom row in the middle figure, etc.). Let ak be the number of triangles when you have k rows and consider the case k 2n, n ≥ 0. S A. Determine the values for a2m where n = 1, 2, 3, and 4. B. Using the results in task A, determine a recurrence relation for a2n, where n ≥ 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Divide an equilateral triangle into a number of triangles that are similar to
the original triangle (ie similar in shape but possibly different size and
possibly rotated)
so that they lie in k rows in the original triangle. If you select k = 2, 4, 8 you
get the following figures (for eg k = 6 you remove the two bottom rows in
the right figure, for k = 3 you delete the bottom row in the
middle figure, etc.).
Let ak be the number of triangles when you have k rows and consider the
case k
=
2n, n ≥ 0.
A. Determine the values for a2m where n = 1, 2, 3, and 4.
B. Using the results in task A, determine a recurrence relation for a2n,
where n ≥ 0.
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