# Tag Info

### 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 ...
• 102k

### 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. (...
• 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 ...
• 16.6k
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}{...
• 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 ...

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