After School

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Presentation Transcript

Using

Geometry

After School

*click to continue

*sources

Geometry By Definition

1. The branch of Mathematics that deals with the deduction of the properties, measurement, the relationships of points, lines, angles, and figures in space from their defining conditions by means of certain assumed properties of space.

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Geometry By Definition

2. The shape or form of a surface or solid

Euclidean Geometry

Earliest Discussion of Geometry.

Has been taught since 300 BC up to modern days.

Beginning levels of Euclidean Geometry are taught in 2 dimensions but can be applied to any finite number of dimensions.

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Non-Euclidean Geometry

Contrasted with Euclidean Geometry, this type can take place in free space as apposed to flat planes.

Works along with Hyperbolic and Elliptical Geometry

Algebraic Geometry

Uses Algebraic Polynomial Equations to define curves and their coordinate points on a graph.

The Process of Problem Solving

Analyzing the Problem

Apply the Solution You Think will Best Solve the Problem

Analyzing the Problem

-- In any situation it is important that you understand the entire problem with which you are faced. It is important to take time to think through the entire situation. --

Possible Solutions

-- Before taking any course of action it is important to think of all the different possible ways to go about solving the problem. --

Applying the Best Solution

-- After thinking about the possible solutions, apply the one you think is appropriate to best solve the problem. If a mistake is made, learn from it and try a different solution to correct the mistake and solve the problem. --

Applications of Problem Solving

Obviously, this process can be applied for working out solutions to geometry related problems: for example, finding the area of a circle with a radius of 2 inches.

Throughout life you will be faced with various problems. Through applying the process learned in geometry, you will be better prepared to respond to these problems.

Computer Graphics

-- The most important feature in computer graphics is geometry. In computer graphics a character is created by a set of geometric shapes which are moved as you view the character from different angles and distorted as the character moves. --

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Medical Imaging

-- Medical Imaging uses advanced technology to obtain pictures to determine exact shapes of parts of your body for medical purposes. For example, a surgeon would prefer to know the exact shape and size of a tumor before removing it. --

Aeronautics

-- Aeronautics uses geometry through an intense understanding of the curvature of the earth that is necessary to make air travel better. --

Essay

Using a text/word editor, write an 100 word essay on how you could use one of the following fun facts of Geometry in a future situation.

Fun Fact 1

Suppose you are creating a hoop that will be one foot bigger in circumference than the circumference of the ball being used to play a game. How much rope would you have to use?

(hint: use formula 2πr)

Fun Fact 2

Suppose you were at the top of a tree house that was 30 ft. off the ground. How would you use geometry to determine how long a cord should be to run a zip line to a safe spot on the ground 200 ft. from the bottom of the tree?

(assume the ground is flat)

Quiz

10 Questions:

Question 1

The first tracings of the study of geometry occurred around what year?

A. 3000 BC

B. 2000 BC

C. 300 BC

D. Yesterday

Question 2

A philosopher named Euclid wrote many texts about Geometry before Pythagoras developed his Theorem.

True

False

Question 3

Non-Euclidean Geometry deals with _______ instead of the triangles of Euclidean Geometry.

A. Squares

B. Octagons

C. Lines

D. Ellipses

Question 4

Part of Critical Thinking is thinking about more than one solution to a problem.

True

False

Question 5

Learning Geometry will not help my Critical Thinking abilities.

True

False

Question 6

The solution I think best applies to the situation will always give me the correct result.

True

False

Question 7

Sonic the Hedgehog is a result of Applied Geometry?

True

False

Question 8

What Medical Industry would be MOST interested in Geometry?

A. Kinesiology

B. Nursing

C. Imaging

D. All of the Above

Question 9

Aeronautics uses Geometry only in airplane design.

True

False

Question 10

What type of Geometry does Aeronautics use the most?

A. Euclidean

B. Non-Euclidean

C. Algebraic

D. None of These

CORRECT!!!

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SORRY!!!

Please Review and Take Quiz Again.

HOORAY!!!

Now You Understand the Importance of Geometry

Sources

http://www.myastrologybook.com/PythagoreanTheorem16c.gif

http://dictionary.reference.com/browse/geometry

Duncan, J. Melville. Third Millennium Chronology. Third Millennium Mathematics. St Lawrence University.

Boyer (1991). “Euclid of Alexandria”, pg 104

Christoph Riedwig, Pythagoras, His Life, Teaching and Influence. Cornell University Press 2005.

Aydin Sayili (1960). “Thabit ibn Qurra’s Generalization of the Pythagorean Theorem” pg. 35-37

Victor J. Katz (1998), History of Mathematics: An Introduction. Pg. 270-271. Addison-Wesley. ISBN 0321016181.

Torretti, Roberto. “Nineteenth Century Geometry.” The Stanford Encyclopedia of Philosophy (Spring 2007). Edward N. Zalta.

http://www.web3dservice.com/andyba/3D/wip/minotaur2.jpg