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In a certain type of tiling called Penrose P3 tiling, two types of rho
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06 May 2021, 00:15
06 May 2021, 00:15
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In a certain type of tiling called Penrose P3 tiling, two types of rhombi fill a space without gaps or overlaps: wide rhombi and narrow rhombi. If five of the wide rhombi can meet symmetrically at a single point, while ten of the narrow rhombi can, what is the ratio of the largest angle in one narrow rhombus to the largest angle in one wide rhombus?
(A) 5 : 2
(B) 2 : 1
(C) 5 : 3
(D) 3 : 2
(E) 4 : 3
(A) 5 : 2
(B) 2 : 1
(C) 5 : 3
(D) 3 : 2
(E) 4 : 3
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In a certain type of tiling called Penrose P3 tiling, two types of rho
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08 May 2021, 07:23
08 May 2021, 07:23
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GeminiHeat wrote:
In a certain type of tiling called Penrose P3 tiling, two types of rhombi fill a space without gaps or overlaps: wide rhombi and narrow rhombi. If five of the wide rhombi can meet symmetrically at a single point, while ten of the narrow rhombi can, what is the ratio of the largest angle in one narrow rhombus to the largest angle in one wide rhombus?
(A) 5 : 2
(B) 2 : 1
(C) 5 : 3
(D) 3 : 2
(E) 4 : 3
(A) 5 : 2
(B) 2 : 1
(C) 5 : 3
(D) 3 : 2
(E) 4 : 3
When five of the wide rhombi meet symmetrically at a single point, the angle subtended would be \(\frac{360}{5} = 72\)
When ten narrow meet at that single point, the angle subtended would be \(\frac{360}{10} = 36\)
Now, In the wide rhombi the largest angle would be \(180 - 72 = 108\), and
In narrow rhombi the largest angle would be \(180 - 36 = 144\)
So the ratio \(= \frac{144}{108}= \frac{4}{3}\)
Hence, option E
General Discussion
In a certain type of tiling called Penrose P3 tiling, two types of rho
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18 Sep 2021, 23:04
18 Sep 2021, 23:04
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I can't expect this on the GRE.
