Euclid's Big Problem - Numberphile
Trisecting angles and calculating cube roots was a big problem for Euclid and his cohorts. Discussed by Zsuzsanna Dancso at MSRI. More links & stuff in full description below ↓↓↓ TRISECT...
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This is the straight edge, except... this is marked. So Euclid's straight edge is just a straight edge. It's not a ruler... And this is a compass... And you can use it to draw circles. Straight edge can do the following: if you have two points in the plane that you have previously somehow constructed or were given to you then you can put the straight edge there and connect them by this fine straight line. And the way to imagine it is that the straight line is infinitely long...and the paper is infinitely big. - So you can't do a line of twenty centimeters...? - Well... sort of. So that's a very good question. Hum... if you're given a line of one centimeter... by... you know... by god... then you can do a line of twenty centimeters, be...
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This is the straight edge, except... this is marked. So Euclid's straight edge is just a straight edge. It's not a ruler... And this is a compass... And you can use it to draw circles. Straight edge can do the following: if you have two points in the plane that you have previously somehow constructed or were given to you then you can put the straight edge there and connect them by this fine straight line. And the way to imagine it is that the straight line is infinitely long...and the paper is infinitely big. - So you can't do a line of twenty centimeters...? - Well... sort of. So that's a very good question. Hum... if you're given a line of one centimeter... by... you know... by god... then you can do a line of twenty centimeters, be...
