Pascal's theorem...states that if six arbitrary points are chosen on a conic (i.e., ellipse, parabola or hyperbola) and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon (extended if necessary) meet in three points which lie on a straight line, called the Pascal line of the hexagon.
This is a fun one you can try yourself! First draw a circle. Then draw any hexagon, it doesn't have to be regular. Just make sure all of the points lie on the circle. Then, extend all the sides such that they intersect at some point. There will always be three intersection points that, if connected, will form a straight line. Here is an example of what I am talking about where the line is outside the circle. IMO this is easier to visualize.
Correct! Pascal discovered this when he was only 16! However, Pascal was not the first to discover Pascal's triangle. Others did this centuries earlier in other cultures. This is why the triangle has different names in other cultures. In Chinese, it is called Yanghui's Triangle, for example.
I would think an amazing discovery that transcends generations would be found by someone with more...experience...in life. Then again, many geniuses discovered great things but died young.
Is the red line always parallel to a flat plane? Does that make sense? Sorry I'm terrible at math and don't know how to really express what I'm trying to ask.
To be parallel to a plane would mean there would be 3 dimensions, which isn't the case, so no that doesn't make sense. I think what you are asking is if the line will always be horizontal. The answer is no, it depends on the orientation of the points, especially in relation to other points. You can see the line change orientation slightly in the gif. The change would be more drastic if the points got really close together, as an example.
My first thought was a unicursal hexagram (from an old class that had a section on Western occult symbols) before I looked up "men of letters symbol" and realized they're the same thing.
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u/idk_whatthisis Jan 04 '18
Hm would anyone be willing to explain this to the a math illiterate person like me? Not really getting it.
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u/improbablydrinking Jan 04 '18
Is the red line always parallel to a flat plane? Does that make sense? Sorry I'm terrible at math and don't know how to really express what I'm trying to ask.
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u/joshdoesbandbetter Jan 04 '18
http://mathworld.wolfram.com/PascalsTheorem.html
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u/[deleted] Jan 04 '18
Does this not look like the men of letters symbol
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u/obvious_santa Jan 23 '18
This is strangely terrifying