Proof by contradiction is a logical mind skill used to reduce a premise or assumption to the absurd, or impossible contradiction. This logical mind game is mastered in logic, but brushed up against in geometry. We play a tug of war game with logic in Geometry. We acknowledge the existence of logic just enough to
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Few modern people can get away with a single name. A few may come to mind, but ancient history are full of those one named wonders. Euclid is one of the most recognizable names in history, and all he did was write a single book. It may have had 13 volumes, but it was a
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Euclidian geometry conjures up images of shapes with all of their angles, lines, tick marks, and sides. The most picturesque branch of high school mathematics is geometry. Geometry after all is the science or art of measuring the earth. It started with the images of the created world around us and is often learned using
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Now that we’ve determined when procedures are necessary and how to not be entangled in the mindless following of said procedures. Let’s go ahead and review a few simple key steps to making a good procedure. First, when you are faced with a series of problems that appear to contain a hidden truth and consistency
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If infinity were odd then two times infinity would be even, but two times infinity is infinity, which is defined as odd. Therefore, infinity is not odd. Another win for proof by contradiction – assume a premise, show how the premise leads to a contradiction, which concludes that the premise is false, therefore, the negation
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