Hello everybody! I haven't posted in a long time. But anyways...
I was working on this problem called 'The fighting fishes of Siam' by the late, great, Sam Loyd and it states that
there are two kinds of fishes, king fish and devil fish. They inevitably attack each other on sight. Three devil fish
counterbalance one king fish. Four devil fish can kill a king fish in 3 minutes with each additional fish making the new group
proportionately quicker. So I did the following... 4*3 = 12, 5*x=12, so x=2.4 or 144 seconds for 5 fish.
But the solution in the back of the book says that each fish added to a group of x fish reduces the time taken by 1/x. So for five fish they say it will take 135 seconds. The time is reduced by 1/4. This seems reasonable, but what if one devil fish killed a king fish in 3 minutes with each additional fish making the new group proportionately quicker? Then two fish would take no time at all! What about three fish then? What's going on?
The eclipses from Algol (an eclipsing binary star) come further apart in time when the Earth is moving away from Algol and closer together in time when the Earth is moving towards Algol, thereby proving that the speed of light is variable and that Einstein's Special Theory of Relativity is wrong.
Welcome back! Check this out.
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.