Euclidean geometry
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| - | | style="text-align: left;" | [[Gaston Bachelard]] showed that new theories integrate old theories in new [[paradigm]]s, changing the sense of concepts (for instance, the concept of [[mass]], used by [[Newton]] and [[Einstein]] in two different senses). Thus, [[non-Euclidean geometry]] did not contradict [[Euclidean geometry]], but integrated it into a larger [[framework]]. | + | | style="text-align: left;" | |
| + | "[[Gaston Bachelard]] showed that new theories integrate old theories in new [[paradigm]]s, changing the sense of concepts (for instance, the concept of [[mass]], used by [[Newton]] and [[Einstein]] in two different senses). Thus, [[non-Euclidean geometry]] did not contradict [[Euclidean geometry]], but integrated it into a larger [[framework]]."--Sholem Stein | ||
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"Gaston Bachelard showed that new theories integrate old theories in new paradigms, changing the sense of concepts (for instance, the concept of mass, used by Newton and Einstein in two different senses). Thus, non-Euclidean geometry did not contradict Euclidean geometry, but integrated it into a larger framework."--Sholem Stein |
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Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclid of Alexandria. Euclid's text Elements is the earliest known systematic discussion of geometry. It has been one of the most influential books in history, as much for its method as for its mathematical content. The method consists of assuming a small set of intuitively appealing axioms, and then proving many other propositions (theorems) from those axioms. Although many of Euclid's results had been stated by earlier Greek mathematicians, Euclid was the first to show how these propositions could be fit together into a comprehensive deductive and logical system.
See also
- Analytic geometry
- Type theory
- Interactive geometry software
- Non-Euclidean geometry
- Ordered geometry
- Incidence geometry
- Metric geometry
- Birkhoff's axioms
- Hilbert's axioms
- Parallel postulate
- Schopenhauer's criticism of the proofs of the Parallel Postulate
- Cartesian coordinate system
Classical theorems
- Ceva's theorem
- Heron's formula
- Nine-point circle
- Pythagorean theorem
- Menelaus' theorem
- Angle bisector theorem
- Butterfly theorem
