2. Axiomatic System
In mathematics, an axiomatic system has a set of axioms, or
rules, that are used to prove other statements or facts.
Henry and Emma are playing
a ball toss game. To play,
Henry and Emma need 1
spinner, 6 balls, 50 tokens,
and a ball toss board.
3. Rules
When you get a ball in a hole, you earn the points
associated with that hole.
Spin the arrow. When the arrow lands on a number, toss
that many balls.
You must stand 3 feet away from the board to toss a ball.
You get 1 token for every 50 points you earn.
5
6
You cannot earn more than 1000 points during a
turn
You lose aturn if you spin a 5.
You need at least 2 people to play.
The first person to earn 2000 points
wins.
7
8
4. Let's Discuss
and Analyze
Together
Do you think some of the rules
contradict each other? Why or
why not?
First Question
Do you think some of the rules
are incomplete? Why or why not?
Second Question
Third Question
Which 2 rules contain repetitive
information?
5. are words , usually readily
understood, that are not
formally explained by means
of more basic words and
concepts.
Undefined
terms
Understanding the Lesson
Geometry is an axiomatic system based on logical reasoning and
axioms.
assign properties to a
mathematical object. A
defined term is a term that
has a definition and can be
explained using undefined
terms and/or defined terms.
Definition
statements that are
accepted as true without
proof.
Axioms or
Postulate
statements or conjectures
that can be proven true
using undefined terms,
definitions, and axioms.
Theorems
6. Example
Question 1
In the fictional country of Rythoth, blue
animals are from the mountains, and red
animals are from the valleys. These animals
are categorized into three distinct classes:
mammals, birds, and reptiles. Mammals are
covered by hair or fur, birds are covered by
feathers, and reptiles are covered by scales.
7.
8. Types of Geometry
Study of geometric figures
without the use of coordinates. It
is sometimes called pure
geometry or Euclidean
geometry.
Synthetic Geometry
Study of geometry using a
coordinate system. It is
sometimes called coordinate
geometry or Cartesian Geometry
Analytic Geometry