The Axiomatic Method in Geometry

Le résumé fourni par la source

We human beings are at home with the physical world—our senses guide our movements and help us estimate sizes. But from earliest times, we have wanted to know things about our physical world that our senses and measuring instruments could not tell us—for example, what is the circumference of the earth? For this, we needed the kinds of geometry we will explore in this book: axiomatic geometry. This means that we start with assumptions people are willing to accept as true (perhaps “for the sake of argument”) and use logical arguments based on these agreed-upon principles, instead of our senses. The process is called deduction and the starting principles are called axioms.

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