/sci/ - Science & Math

>>11925814

>>11243911
I thought Thales' Theorem was pretty cool when I first learned about it.

>>9109066
>Thales' theorem

>In geometry, Thales' theorem states that if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ∠ABC is a right angle. Thales' theorem is a special case of the inscribed angle theorem, and is mentioned and proved as part of the 31st proposition, in the third book of Euclid's Elements.
I don't know why but I always thought that was pretty cool.

>>4948038

There are tons of ways to construct sqrt(2). It's one of the first things you learn in constructivist geometry. Here is a neat method that can be used to construct the sqrt of any number.

Draw a circle with a diameter of 3. Now draw a line cutting the circle in half. From the new line, at 1 unit in from the edge (remember, this line is 3 units long because it is the diameter), draw a line perpendicular extending vertically till it reaches the edge of the circle. Draw the two new lines from the intersections of the diameter line with the circle to the intersection of the vertical line with the circle. These two new lines with the first diameter line now make a right angle in accordance to thales theorem. The vertical line splits said right triangle into two congruent right angles. You can now do the algebra fairly trivially with the congruent triangles to show that the length of the vertical line is sqrt(2). By repeating the process with a circle of diameter n it is possible to construct a line of length sqrt(n). I'll leave this up to you to show so that you may hopefully learn something.

>>4907600

Mathematics are the same regardless of base.

What base is this triangle in.