LESSON cbnsssujndeeijfsethfor vdnfor 1.pptx

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1. Describing Mathematical Systems Lesson 1

2. AXIOMATIC STRUCTURE OF A MATHEMATICAL SYSTEM IN GEOMETRY

3. AXIOMATIC STRUCTURE OF A MATHEMATICAL SYSTEM IN GEOMETRY It is a set of undefined and defined terms, from which some or all axioms/postulates can be used together to logically derive and prove theorems.

4. THE UNDEFINED TERMS The three undefined terms in Geometry are the basic building blocks of a mathematical system. The three terms are point, line, and plane. These are the words that are accepted as starting concepts of a mathematical system.

5. POINT Indicator of position or location. A point does not occupy an area. It has no dimension. Zero width, length or depth.

6. POINT

7. LINE A collection of continuous points that extends endlessly in both directions. It has only one dimension (length). A line can be defined by two points and denoted by a segment with arrows on either end.

8. LINE

9. PLANE A flat slanted closed four-sided figure made of a set of points that extends without end in all directions. It has endless length and width but no thickness. It has two dimensions – length and width.

10. PLANE

11. THE DEFINED TERMS Defined terms are terms in Geometry that has a category and list of critical attributes. They can be described using known terms (undefined terms) such as point, line, or plane.