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The Anatomy of Black Holes - Page 23

Inevitable Mathematics

Scientists believe that if an object reaches a critical radius near a black hole, the object will inevitably be drawn into the singularity. In mathematics, a similar situation can occur. Some mathematical expressions and operations will result in a numerical 'black hole' no matter where you start!

A. Follow the below procedure starting with a positive integer. We show you the results for the beginning values of 5 and 7.

numerical black hole

 

Why does this procedure always give the answer 4? Let us examine the steps.

Go through the procedure again with the starting value of "B".

numerical black hole

Notice that the final result is 4, regardless of the initial value. That is, all beginning numbers fall into the 'black hole' 4.

Now it is your turn. Can you create a numerical 'black hole' whose value is always 10?

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A service of the High Energy Astrophysics Science Archive Research Center (HEASARC), Dr. Alan Smale (Director), within the Astrophysics Science Division (ASD) at NASA/GSFC

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