this is what i did for (1)
If two points have rational coefficients (a,b) and (c,d), the line between them has equation:
x(b-d) - y(a-c) = (bc - ad)
this is where I'm stuck. I'm not sure how to proof the coefficients of the equation are rational
Hi guys, I'm having trouble solving the following questions.
1) Show that the line through two rational points has an equation with rational coefficients
2) show that a circle whose center is a rational point and whose radius is rational has an equation with rational coefficient.
Cheers
Guys please help me with this:
1) Show that the slice z=c of the sphere x² + y² + z² =1 has the same area as the slice z=c of the cylinder x² + y² =1 outside the cone x² + y² = z².
2) Deduce from the previous problem, and the known volume of the cone, that the volume of the sphere is 2/3...