History of MathematicsPrentice Hall GeometryGeometryAugust 2009

Mayans MEXICOMayans are from ____________.Base 20 systemOne of the 1st cultures to invent _________.Their calendar had 18 months a year; 20 days a monthZERO

According to the Mayans:The WORLD will END on… The WORLD will END on… 21 DECEMBER 2012

RomansRoman Numeral SystemI, II, III, IV, V,…,X, L, C, D, M,…The system is based on Subtractive PairsThe Line above Roman Numerals means multiply by a thousand

Egyptians1st to have fractions! Geometry invented by EgyptiansGeo means earth; meter comes from measuresUsed geometry to measure land to assess taxes

EgyptiansCame closest to developing pi pi is the ratio of diameter of a circle to the circumference of the circle

Famous MathematiciansRene DescartesPierre de FermatBlaise PascalRobert HookeIsaac NewtonJames BernoulliGirolamoSaccheriJohn BernoulliChristian GoldbachLeonhard EulerJoseph Louise LagrangeCarl Freidrich GaussBernhard RiemannDavid HilbertJohn von NeumannThales of MiletusPythagoras of SamosHippocrates of ChiosEuclidArchimedesGalileo Galilei

QUIZQuizWhen is the world going to end according to the Mayans?Where are the Mayans from?What is the system of Roman Numerals based on?Egyptians invented _______ for what two reasons?What base system do we use today?

Geometry Three Types of Geometry:Euclidean (what we will study)Non- Euclidean Elliptic Geometry (Spherical Geometry)Hyperbolic Geometry

EuclideanGeometry

Undefined Terms can be described but cannot be given precise definitions using simpler known terms.3 Main Undefined Terms:Undefined TermsPoint is thought to be a circular dot that is shrunk until it has no size. Line is thought to be a wire stretched as tightly as possible of infinite length having no thickness.Plane is thought to be a sheet of paper that has no thickness, stretched tightly , and extending infinitely in all directions.

Using the undefined terms (point, line, plane)allows us to define other terms in geometry, e.g. space: a set of all pointsDefinitions

Postulates and axioms are one in the same.They are accepted as statements of fact.Postulates and Axioms

TheoremsTheorems are results that are deduced from undefined terms, definitions, postulates, and/ or results that follow from them.

EuclideanGeometry

how to solve geometry?Scientific Method?Ask a QuestionDo Background ResearchConstruct a HypothesisTest Your Hypothesis by Doing an ExperimentAnalyze Your Data and Draw a ConclusionCommunicate Your Results

how to solve geometry?Four Steps:Understand the ProblemDevise a PlanCarry Out the PlanLook Back

1. Understand the ProblemIs it clear to you what is to be found?Do you understand the terminology?Is there enough information?Is there irrelevant information?Are there any restrictions or special conditions to be considered?

2. Devise a Plan.How should the problem be approached?Does the problem appear similar to any others you have solved?What strategy might you use to solve the problem?

3. Carry Out the PlanApply the strategy or course of action chosen in Step 2 until a solution is found or you decide to try another strategy

4. Look BackIs your solution correct?Do you see another way to solve the problem?Can your results be extended to a more general case?

Some Strategies…Draw a picture!Guess and check.Use a variable.Look for a pattern.Make a table.Solve a simpler problem.

What to do when you start working a geometry problem?Understand the problem.Devise a plan.Carry out the plan.Look Back.

POINTLINEBAAlABLine l

planeBACPlane ABC or Plane PP