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  • 1 Post By v8archie
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February 9th, 2016, 11:55 AM   #1
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Question Is there a name for this? Can it be expressed algebraically?

I'm not sure if this has a name but:

6420 / 420 = 15.285714285714285714285714285714

420 / 15.285714285714285714285714285714 = 27.476635514018691588785046728972

27.476635514018691588785046728972 / 420 = 0.06542056074766355140186915887851

420 / 0.06542056074766355140186915887851 = 6419.9999999 or 6420

Another example:

5000 / 200 = 25
200 / 25 = 8
8 / 200 = 0.04
200 / 0.04 = 5000

Is there a name for this?
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February 9th, 2016, 02:46 PM   #2
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Division.
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February 9th, 2016, 03:07 PM   #3
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$${a \over b}=c \\ {b \over c}={b \over {a \over b}}= {b^2 \over a} \\ {{b^2 \over a} \over b}={b \over a} \\ {b \over {b \over a}}=a$$

So it's just a pattern of division that works for any non-zero $a$ and $b$.
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February 10th, 2016, 03:31 AM   #4
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Just wanted to say, I know it's division (obviously), but I wanted to know if repeatedly dividing like this, and ending up with the number you started with, I was wondering if this kind of pattern had a name. Thanks anyway.
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