Yin and Yang
Yin and Yang is one of the world's oldest religious symbols.
Do you know there is an elegant way of drawing one straight line across the circle so that it exactly bisects the areas of the Yin and Yang?
Do you know there is an elegant way of drawing one straight line across the circle so that it exactly bisects the areas of the Yin and Yang?
Labels: thinktank
posted by Rajesh Lal at
11:02 PM
13 Comments:
No.
I did not know that.
Next question please.
Ditto
that line would pass through the centres of mass of both white and black portion
Dont remember the formula for the centre of mass for a semi circle though
Just a horizontal line passing through the centre? This 'bisects the two areas'
To exactly bisect the areas of each of the Yin's and the Yang's one must draw a line at a 45 degree angle from the top left quadrant to bottom right quadrant in the picture shown.
blah blah blah
Ha Ha Ha!
Start the line from where the two colors meet at the edge of the circle and draw a line to the other end where the black and white meet at the edge of the circle
Bean has it right. Here is the proof:
Let the circle center be at point O. Let a diameter through O have point A at the top (where black/white meet) and B at the bottom (where black/white also meet). Draw two semi-circles with diameters AO (top black/white boundary) and BO (bottom black/white boundary). Draw another diameter COD of the circle perpendicular to AOB from left to right.
Each of the circles with diameters AO and BO have areas of 1/4 of the big circle. Therefore the areas to the left and right of the two circles also measure 1/4 of the area of the big circle.
Draw a line EOF at 45 deg. to AOB from lower right to upper left.
If you did all the drawing, you can see that the white area to the right of EOF consists of half of a smaller circle (as divided by line AO) plus half of the upper left quarter of the big circle (the quarter defined by lines AO and CO and divided by EOF) for a total of 1/8 + 1/8 = 1/4 of the large circle's area or half of the white area, so it divides the Yin in half. The Yang area is similarly divided.
See the illustration for the above.
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why bisect it anyway?
Why comment anyway
weener
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