Most of us love manipulating things. Yet, the word manipulate is a rather new one. The first recorded instance of its use was less than 200 years ago, in 1834. It derives ultimately from the Latin manipulus which meant a “full hand” or “handful” … and we certainly like to keep our hands full (or occupied).
This is a wonderful form of play and discovery … not simply arranging shapes, but changing them or arranging/combining them in three dimensions.
The match sticks depicted here have been cleverly manipulated and hint at a relationship. Mathematical relationships are different from the one hinted at here, of course, but I thought the image would present a clever visual pun … that we manipulate objects to discover or show relationships between things!
Balancing a Coin
How can you balance a twenty cent piece on the (vertical) edge of a ten dollar note?
This is not a particularly difficult challenge, but it will give you a 'taste' for manipulation questions.
Carefully examine what you HAVE been asked to do and then examine your assumptions and whether you have been asked explicity NOT to do certain things. Sometimes, we assume that there are more restrictions than there really are!
When you are ready to compare your solution with my one, please click here.
I enjoyed your presentation and no it wasn’t too long. Each subtraction algorithm has its merit as you demostrated, but after learning the “one up and one down” method, I’m employing it because of its speed and ease of usage. Even my wife, who hates mathematics with a passion, thinks it’s too easy. I look forward to your future presentations on both multiplication and number theory. I read an introduction text book some twenty five years ago on number theory by Oystein Ore who taught at Yale for better than twenty years. So in closing, please produce these lectures and the longer the better. Thanks.
Dennis Bell (on a CCM YouTube video about How to Subtract (Large) Numbers Easily)
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