Explore Related Concepts

Best Results From Wikipedia Yahoo Answers Youtube

From Wikipedia




Logical axioms are usually statements that are taken to be universally true (e.g., A and B implies A), while non-logical axioms (e.g., ) are actually defining properties for the domain of a specific mathematical theory (such as arithmetic). When used in the latter sense, "axiom," "postulate", and "assumption" may be used interchangeably. In general, a non-logical axiom is not a self-evident truth, but rather a formal logical expression used in deduction to build a mathematical theory. To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms). There are typically multiple ways to axiomatize a given mathematical domain.



The word "axiom" comes from the Greek word á¼€Î¾Î¯Ï‰Î¼Î± (axioma), a verbal noun from the verb á¼€Î¾Î¹ÏŒÎµÎ¹Î½ (axioein), meaning "to deem worthy", but also "to require", which in turn comes from á¼„Î¾Î¹Î¿Ï‚ (axios), meaning "being in balance", and hence "having (the same) value (as)", "worthy", "proper". Among the ancient Greekphilosophers an axiom was a claim which could be seen to be true without any need for proof.



Historical development

Early Greeks



An â€œaxiomâ€�, in classical terminology, referred to a self-evident assumption common to many branches of science. A good example would be the assertion that When an equal amount is taken from equals, an equal amount results.



# It is possible to extend a line segment continuously in a straight line.

Question:I would like to know an alternate way to illustrate the Angle Addition Postulate. I've already made a typical acute angle with points ABC, and with D sticking out diagonally from point B, the vertex. But I would like another one or two samples of different kinds of angles (not acute) Thank you.


Answers:When two angles share a common ray, say AB, where A is the vertex of both angles, and the angles are on opposite sides of AB (for example angle CAB is opening on the left side of AB and angle DAB opening on the right side of AB), then angle CAD = angle CAB + angle ABD. If B is on segment AC and between A and B then the sum of the lengths AB and BC is equal to the length of segment AC. AB+BC+AC. Both are really very obvious results similar to saying if I split a pile of rocks into two piles of rocks then the the number of rocks in the original pile is equal to the sum of the number of rocks in the two piles created from the first pile.

Question:What is the definition of an addition postulate? I don't need examples of problems because I understand that part.

Answers:Please clarify with the type of addition postulate. For example, Definition of Angle Addition Postulate Angle Addition Postulate states that if a point S lies in the interior of PQR, then PQS + SQR = PQR. ----------------------- Segment Addition Postulate If B is between A and C, then AB + BC = AC. There are several others.


Answers:simple trig? I barely remember back that far but heres your answer enjoy~

From Youtube

How to Use the Arc Addition Postulate to Find Arc Lengths :This video math lesson teaches the arc addition postulate. The arc addition postulate states the measures of two adjacent arcs can be added. This is similar to the segment and angle addition postulates. The example in this geometry video lesson involves finding the the measures of two arcs in a diagram. One central angle measure is given and one arc measure is given.

Angle Addition Postulate - YourTeacher.com - Geometry Help :For a complete lesson on angle addition postulate and angle bisector, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn the angle addition postulate and the definition of an angle bisector. Students also learn the definitions of congruent angles and adjacent angles. Students then use algebra to find missing angle measures and answer various other questions related to angle bisectors, congruent angles, adjacent angles, and segment bisectors.