Definitions and concepts
Download
Report
Transcript Definitions and concepts
Definitions and concepts
MA418
Spring 2010
McAllister
What are ……..?
Undefined terms
Definitions
Postulates and axioms
Theorems
An axiomatic system
Undefined terms
Figures or ideas that can be described, but
cannot be given precise definitions
◦ Point – location in space. 0-dimension
Indicated by a dot, Label with Capital Letters
A
◦ Line – infinite set of points. 1 – dimension
Indicated by
Label with 2 points or a lower case letter.
◦ Plane – sheet of points. 2 – dimensions
Definitions
Figures and objects that are described in
terms of undefined terms, previously
defined terms, and postulates.
We DEFINE space to be the set of all
points.
We DEFINE a geometric figure to be a
subset of space. (p. 39)
Postulates (axioms)
Statements we assume to be true
State relationships among defined and
undefined terms.
◦ Every line contains at least two distinct points
◦ Two points are contained in one and only one
line
◦ If two points are in a plane, then the line
containing these points is also in the plane
(p.40)
Theorems
Deductions
that can be made from
undefined terms, definitions, postulates,
and already proven theorems
◦ The sum of the measures of the angles in a
triangle is 180⁰. (p. 66)
◦ The sum of the measures of the vertex
angles in a polygon with n sides is
(n2)180⁰. (p.68)
Axiomatic system
An
idea structure
Begins with a small set of undefined
terms and builds on them to produce
definitions, postulates and theorems.
◦ Euclidean
◦ Non-Euclidean (pp. 555 – 565)
Taxicab geometry (p. 560)