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File: ellipse_diagram.png (7KB, 648x412px) Image search:
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For any ellipse centered at the origin, the line, y = mx, splits the ellipse in exactly 2, regardless of the value of m. Why is that?
Is it related to the fact that if the ellipse was a circle, the property would hold because of the symmetry of the circle, and then under the transformation of stretching the circle, the ratio of the areas created by the line does not change? If so, how can one express this mathematically?
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>>8736097
If you reflect the image by the x- and y-axes you get the same picture with red and green inverted.
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>>8736110
same for any square.
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>>8736117
Same for any shape with 2k (where k belongs to positive integers) corners and has a symmetriline at x=0
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>>8736121
A symmetriline has to be congruent with x=0 and y=0, sorry.
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>>8736097
Don't let the symmetry fool you. Cover the lower half and then tell me what's so intriguing?
Thread posts: 7
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Thread images: 1