Enumerate the major strenghts & weaknesses of Euclidean geometry.?

Question

Math questions

Answer 1

OK, Jeff, you're making my giant green brain hurt!

Answer 2

Euclidean geometry was developed using a planar model of space. It is very advantageous for most of the math that we have to do in our everyday lives and even in specialized professions like architecture.

However, it breaks down when we apply it to other models of space, say a spherical or conical version. Then we must ask ourselves all over again, 'what constitutes a line and how do lines function together?' There are several types of non-euclidean geometries that address these problems. If you want to know more, I recommend a book called Mathematics for the Nonmathematician by Morris Kline.

Finally, we still don't know what occurs very, very far into outer space. We don't know how far the Euclidean axioms will continue to be correct as we move to the edges of our knowledge about the universe.

Answer 3

Euclidean geometry was consistently held in high esteem in England. Robert Simson (1687-1768) published the first edition of his English translation of the Elements of Euclid in 1756, and this translation was highly regarded for its precision and accuracy. Although not the first English translation, Simson's work served as the foundation for most subsequent geometry texts, and it was probably well known to both Cowley and Jones. In his preface to the third edition of Cowley's book, Wiliam Jones alludes to "that dark and groveling method, the rule only." He is referring to the longstanding belief that all geometric constructions had to be effected by a ruler and compasses only, and that all other methods were mechanical and not geometric. Leonardo da Vinci had made advances in construction using other means than the rule and compass, but it was the artist Albrecht Durer who showed that it was possible to construct regular and semi-regular solids out of paper by drawing the bounding polygons all in one piece and then folding the figures along the connected edges.

Answer 4

Oh, but the possibilities and enumerations are endless good fellow, but we shall not forthwith enumerate here!