Concept explainers
Here we celebrate the power of algebra as a powerful way of finding unknown quantities by naming them, of expressing infinitely many relationships and connections clearly and succinctly, and of uncovering pattern and structure.
New knots in the box. Your math instructor has a new box of knots. The number of unknots in the box is x, the number of trefoil knots in the box is y, and the number of figure-eight knots is z. You take all the knots out of the box and display them so each looks like the unknot, trefoil or figure-eight knot illustrated in Mindscape 20. Suppose you also know there are twice as many unknots as trefoil knots. If there are a total of 36 knots and 72 crossings, how many knots are there of each type?
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The Heart of Mathematics: An Invitation to Effective Thinking
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