number of sleep cycles = nearest integer to (500+20) / 100
Know Your Sleep, Own Your Nights
Flavian Hautbois

Erratum: this formula was incorrectly written with 500–20 instead of 500+20. The demonstration is the following:

500 = (average length of sleep cycle — 20)+(total number of sleep cycles — 1)*(average length of sleep cycle)

500 = total number of sleep cycles*(average length of sleep cycle — 20)

total number of sleep cycles = 520/average length of sleep cycle

with the condition that the number of cycles be an integer, and then we have

real length of subsequent sleep cycle = 520/total number of sleep cycles

All this demonstration holds true given the hypothesis:

length of first sleep cycle = length of subsequent sleep cycle — 20

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