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!
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 have been watching your “Integration technique” videos with high expectation and excitement. They never fail to give me a lot of joy and much pleasure. You must have been one hell of teacher at your time! … just continue making highly enjoyable and intellectually stimulating videos. … Unfortunately, what you learn at the university, you hardly ever see again in your office job. That is why I try to repeat some thing I learned: to enjoy it a bit more, to marvel upon beauty, and to keep my brain sharp. There is where your videos come in perfectly: interesting, amusing and thought provoking problems neatly presented. … You do your best to share your passion, knowledge and experience. The least I can do is to say an honest “Thank you!” As I said, your videos give me much pleasure. You may freely let other people know that. … Rest assured that I shall be watching your videos in the future. With joy and excitement. And I shall comment on them from time to time. You just continue making them.
Zoran V (in private correspondence via YouTube, quoted with permission)
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