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 never understood calculus faster than I did from your 25 min video …
Ghadad B (on a CCM YouTube video about the Chain Rule)
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