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bob012345 reacted to anuttarasammyak's post in the thread High School Area of Overlapping Squares with
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The formula for the 2nd and the 3rd case is written as $$\frac{a^2+s^2-as(\sin\theta + \cos\theta)}{2 \sin\theta \cos\theta}$$ which is... -
bob012345 replied to the thread High School Area of Overlapping Squares.Interesting observation! It appears so if both values are within the range of the functions. Looking at ##(a,s)## being (4,5) vs...
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bob012345 reacted to anuttarasammyak's post in the thread High School Area of Overlapping Squares with Like.
The answers for the first case and the 4th case are symmetric for exchange of s and a. May we expect the same for the 2nd and the 3rd...
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bob012345 replied to the thread High School Area of Overlapping Squares.I worked out the overlap of the two squares as a function of angle. Given ##a## is the half edge length of the original square and...
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This is my interpretation of the problem statement in the original post.
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bob012345 replied to the thread High School Area of Overlapping Squares.Agreed. Now the larger square is the 1m square. The overlap depends on the relative orientation until ##s## shrinks to...
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bob012345 reacted to anuttarasammyak's post in the thread High School Area of Overlapping Squares with Like.
$$s=\sqrt{2}/2$$is the minimum value satisfying it though not larger any more. And also $$s=\frac{1}{2\sqrt{2}} $$is the maximum.
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bob012345 replied to the thread High School Area of Overlapping Squares.The next level is if we let the length ##s## of the larger square vary, what range of values of ##s## will your statement not be true?
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bob012345 reacted to anuttarasammyak's post in the thread High School Area of Overlapping Squares with Like.
It seems not necessary. For any angle configuration we get the same result.
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bob012345 reacted to kuruman's post in the thread High School Area of Overlapping Squares with Like.
A figure sure helps.
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Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the...
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bob012345 reacted to Charles Link's post in the thread Undergrad Trigonometry problem of interest with Like.
Sometimes it's simpler to use degrees rather than radians for the measurement of angles.
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bob012345 replied to the thread High School More similar triangle problems.Well that explains my little mystery from post #18. Here is the curve for the total area of the triangle for c=d normalized to the...
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bob012345 reacted to PAllen's post in the thread High School More similar triangle problems with Like.
Regarding post #21, the formula given for area minimizing ##\theta## simplifies to ##\tan\theta=c/d##. The minimum area just becomes...
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bob012345 reacted to Gavran's post in the thread High School More similar triangle problems with Like.
All right. Based on post #19, there are the next steps. $$...
