The Grammarphobia Blog

Don’t know much geometry

Q: I was watching an old “Star Trek” episode in which one of the characters referred to power levels as increasing “geometrically.” (This from a supposed graduate of Starfleet Academy.) Shouldn’t the levels have increased “exponentially”?

A: These two terms can be confusing, and most dictionaries aren’t a help. Despite what you seem to think, however, “geometrically” and “exponentially” can refer to the same kind of numeric growth. Here’s what I mean.

When numbers in a series increase by addition, they form an “arithmetic” (accent on the third syllable) or “linear” sequence. Example: 2, 4, 6, 8, 10, 12. (This sequence has a constant difference of 2.)

When numbers in a series increase by multiplication, they form a “geometric” or “exponential” sequence. Example: 3, 6, 12, 24, 48. (This sequence has a constant ratio of 2.)

I hope this helps.

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