Inverted and Recurring Words

These math words popped up during yesterday's blog: Inverse [or Inverted] and Recur [or Recurring].  Let's invert the order and define Recur first, okay? (Is this a clever way to define inverse, or what?)

Recurring means continuing, on-going, repeating repeating repeating. 

In math we could use it like this:

Give the value 2/3 in decimal form. Answer = .66666666  In this case, the 6 is a recurring number.

We could use it like this in a family:

Dave and Katy had a recurring argument over the size of Katy's mobile phone bill!

Or like this:

In her recurring dream, she would always have to give a speech to a large group of people ...

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Now let's get back to inverse. It means turn over; opposite; reverse, negative, "the other way".

In math, we can use it like this:

Give the inverse of the fraction 2/3: Answer = 3/2  Another term for this is reciprocal.

Notice that the product [multiplicative inverse] of these two numbers is one. That means zero can't have a reciprocal, because 0 times a real number is 0, not 1.

Or we can use inverse like this:

Give the inverse of the real number -5: Answer = 5

Notice that the sum [additive inverse] of these two numbers is always zero.

This discussion has reminded me of two more words that we sometimes use in the math curriculum - most often describing coins. These are obverse and reverse.

Obverse means turned to face you. Reverse means turned to face the other way.

We would use it like this:

Which side of a coin is the obverse? The face or "heads" is always the obverse side. In the case of coins without a portrait (the Euro) the obverse is the common side, shared by all variations of the coin.

Which side of a coin is the reverse? The back side or "tails" is always called the reverse.  

These photos show a Roman coin that my friend Ken located in a field in Dorset, England. He gives most of them to the farmers who own the fields, or to museums.