Squaring a triangle (greek problem)

So, I am taking a history of mathematics course, and apparently the greeks could square a triangle by using just a ruler and compass. How did they do this? I figured out that if bh/2=area of triange then √(2bh)/2=√area of that triangle

But I cant seem to figure out how they did this with ruler and compass. Im looking at right triangles so I can someone use pythagorean squares but I havent been able to do it,

Any help will be appreciated,

thanks

Re: Squaring a triangle (greek problem)

What do you mean by "apparently the greeks could square a triangle by using just a ruler and compass"? You mean given any right triangle (Triangle 1), they could draw a second triangle (Triangle 2) so that (area of Triangle 2)x(area of Triangle 2) = area of Triangle 1? Are these triangles supposed to be similar (have the same angles)? Or is the second triangle arbitrary?

Re: Squaring a triangle (greek problem)

Quote:

Originally Posted by

**calculuskid1** So, I am taking a history of mathematics course, and apparently the greeks could square a triangle by using just a ruler and compass. How did they do this? I figured out that if bh/2=area of triange then √(2bh)/2=√area of that triangle

But I cant seem to figure out how they did this with ruler and compass. Im looking at right triangles so I can someone use pythagorean squares but I havent been able to do it,

Any help will be appreciated,

thanks

chack this site Triangle Squaring -- from Wolfram MathWorld