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yungman
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What is the difference between the Euclidean Geometry and the simple plane geometry? They seems to work with flat planes.
yungman said:Everything about Euclidean geometry sounds like just simple plane geometry I learned long time ago …
tiny-tim said:Hi Alan!
Yes it is … different name, same thing!
Euclidean geometry is a type of geometry that studies the properties of objects in a flat, two-dimensional space. Plane geometry, on the other hand, is a type of geometry that studies the properties of objects in a three-dimensional space.
The basic principles of Euclidean geometry include the concepts of points, lines, and planes, as well as the postulates of equality, symmetry, and parallelism. It also involves the use of axioms and theorems to prove geometric relationships.
Euclidean geometry has many practical applications in fields such as architecture, engineering, and design. It is used to create accurate measurements and designs for structures and objects in the physical world.
No, Euclidean geometry is limited to studying objects in a flat, two-dimensional space. It cannot be applied to non-flat surfaces, such as spheres or curved surfaces.
One famous example is the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Another example is Euclid's Elements, a mathematical treatise that is considered the foundational work of Euclidean geometry.