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You trace a circle (the red one) using a pen with a thick circular end. Both the outside and inside borders of the trace are also circles (in blue):
If you trace any ellipse using the same kind of pen, will the outside and inside borders also be ellipses?
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Imagine two stars A and B forming a binary star system, where they revolve around a common point in space under their mutual gravitational attraction alone. If A is heavier than B and they both revolve in circular orbits, then which star will have a smaller orbital radius?
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The first few powers of 101 all begin with 1, as highlighted by red colors below: 1011101210131014====⋮.101102011030301104060401 Is that always the case for all powers of 101?
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If a+a2+a3+a4+a5+⋯ is a positive number, then which of the following is larger,
a+a3+a5+a7+⋯ora2+a4+a6+a8+⋯?
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(1+x1)x+1=(1+19991)1999
Find the sum of all real x such that the above equation is true.
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