Q: Is geometry called a geometer? ¶
Q: Was geometry recognized? ¶
Q: Is geometry geometry in its classical sense? ¶
Q: Was geometry then expressed by Riemann in his 1867 inauguration lecture Über die Hypothesen? ¶
A: Yes, and welche der Geometrie zu Grunde liegen , published only after his death.
Q: Is geometry a geometry without measurement or parallel lines? ¶
A: Yes, and just the study of how points are related to each other.
Q: Is geometry an active field combining algebraic geometry and number theory? ¶
Q: Is geometry among more applied subfields of modern algebraic geometry? ¶
Q: Was geometry further enriched by the study of the intrinsic structure of geometric objects that originated with Euler and Gauss and led to the creation of topology and differential geometry? ¶
Q: Is geometry concerned mainly with questions of relative position of simple geometric objects? ¶
A: Yes, such as points, lines and circles.
Q: Was geometry synthetic a priori? ¶
Q: Is geometry described? ¶
Q: Was geometry its rigor? ¶
A: Yes, and it has come to be known as axiomatic or synthetic geometry.
Q: Is geometry intrinsic? ¶
A: Yes, and meaning that the spaces it considers are smooth manifolds whose geometric structure is governed by a Riemannian metric, which determines how distances are measured near each point, and not a priori parts of some ambient flat Euclidean space.
Q: Was geometry revolutionized by Euclid? ¶
A: Yes, and whose Elements, widely considered the most successful and influential textbook of all time, introduced mathematical rigor through the axiomatic method and is the earliest example of the format still used in mathematics today, that of definition, axiom, theorem, and proof.
Q: Was geometry put into an axiomatic form by Euclid? ¶
A: Yes, and whose treatment, Euclid's Elements, set a standard for many centuries to follow.
Q: Was geometry a collection of empirically discovered principles concerning lengths? ¶
A: Yes, and angles, areas, and volumes, which were developed to meet some practical need in surveying, construction, astronomy, and various crafts.
Q: Is geometry the Egyptian Rhind Papyrus and Moscow Papyrus , the Babylonian clay tablets such as Plimpton 322? ¶
A: Yes, For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, or frustum.
Q: Is geometry the modern incarnation of the Cartesian geometry of co-ordinates? ¶
Q: Is geometry nearly as old as the science of geometry itself? ¶