there is no easier way to learn Geometry
A two column proof....used only by high school teachers, to make their students bettter at organizing their thoughts, as it can be pretty overwhelming when you are jsut starting to do them. However, in the real world, no one actually uses this method to prove stuff. They use paragraph proofs, where you write out the proofs as if you were writing a paragraph, explaining your reasons for each thing along the way.
Aristotle considered geometry one of the most important sciences, and did some work with point and line planar geometry. He also used geometry as a way into sciences where he did more work, like optics and mechanics.
Exactly in the same way as we use geometry today for their constructions of pyramids and land measurements.
It's great importance of geometry as far as everything is measured in some way and in civil structures as buildings and properties geometry has great importance so there's no disaster.
A proof in geometry is basically proving a specific thing, like this segement is congruent to this, or proving something is a parallelogram....there are all sorts of very different kinds of proofs. Proofs have to be logical to everyone, and following a reasonable thinking path, using definitions, postulates, and theorems as reasons along the way. Most commonly written in paragraph form(in the real world) and 2-column proofs in middle/high school, apparently to organize your thinking when you first start doing them. An indirect proof is a way to do some proofs, like if it asks you to prove AX is not congruent to XY, then you would assume it is, and see how it goes from there, till you find a contradiction, and so the original assumption you made is false.
there is no easier way to learn Geometry
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A two column proof....used only by high school teachers, to make their students bettter at organizing their thoughts, as it can be pretty overwhelming when you are jsut starting to do them. However, in the real world, no one actually uses this method to prove stuff. They use paragraph proofs, where you write out the proofs as if you were writing a paragraph, explaining your reasons for each thing along the way.
It is certainly possible to examine questions of geometry using the art of M.C. Escher, although this would be a very unusual means of approaching the subject. There is doubtlessly some advantage to doing it this way, since many people are bored by the more conventional approach to teaching geometry. Escher is interesting.
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Aristotle considered geometry one of the most important sciences, and did some work with point and line planar geometry. He also used geometry as a way into sciences where he did more work, like optics and mechanics.
It is not known. Euclid's Elements is famous for setting out geometry in a systematic and axiomatic way, his book was by no means the first on geometry.
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Euclid
Euclid
When asked by King Ptolemy about an easier way to learn mathematics, it is claimed that Euclid told him that "There is no royal way to geometry".