Hot answers tagged

3 votes

geometrical/physical interpretation of multiplication of real numbers (including negative)

There are a couple of different ways to express multiplication using geometry. One somewhat physical interpretation of multiplication involves stretching/compressing/reflecting the number line. For ...
user avatar
  • 102k
2 votes

How much of the earth can see the moon?

Let $R=6371km$ be the radius of the earth $r= 1737km$ be the radius of the moon $d= 384467km$ be the distance between the earth and moon. Consider the figure below: $A$ is the centre of the earth. (...
user avatar
  • 545
1 vote

geometrical/physical interpretation of multiplication of real numbers (including negative)

I believe the geometrical interpretation still work, if you take the signed area of the rectangle. So, let's define an "oriented" rectangle as a rectangle with a particular orientation of ...
user avatar
1 vote

Solving $\ddot r=-\frac{GM}{r^2}$

To solve, begin by multiplying both sides by $r'$ (assuming $r'(0) \ne 0$). $$r'r'' = -\frac{GM}{r^2}r'.$$ Now, $$\frac{1}{2}\frac{d}{dt}(r'^2) = -\frac{GM}{r^2}r'.$$ $$\frac{1}{2}d(r'^2) = -\frac{GM}{...
user avatar
  • 1,195
1 vote

How much of the earth can see the moon?

Attached pic for referenceShort and approximate: The distance between earth and moon is about 384,400 km, whereas the radius of the earth is near 6,400 km which is very small compared to the previous ...
user avatar

Only top scored, non community-wiki answers of a minimum length are eligible