Using. Geometry. After School. *click to continue. Table of Contents. *to return to this menu click the following. *sources. Geometry. # 1. Geometry By Definition.
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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.
2. The shape or form of a surface or solid
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.
Contrasted with Euclidean Geometry, this type can take place in free space as apposed to flat planes.
Works along with Hyperbolic and Elliptical Geometry
Uses Algebraic Polynomial Equations to define curves and their coordinate points on a graph.
Analyzing the Problem
Think About all Possible Solutions
Apply the Solution You Think will Best Solve 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. --
-- Before taking any course of action it is important to think of all the different possible ways to go about solving the problem. --
-- 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. --
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.
-- 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. --
-- 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 uses geometry through an intense understanding of the curvature of the earth that is necessary to make air travel better. --
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.
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)
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)
3 about Geometry in General
3 about Critical Thinking
3 about Future Job Possibilities
1 about All Learning Combined
* If answered correctly proceed
* If answered incorrectly please study and try again
The first tracings of the study of geometry occurred around what year?
A. 3000 BC
B. 2000 BC
C. 300 BC
A philosopher named Euclid wrote many texts about Geometry before Pythagoras developed his Theorem.
Non-Euclidean Geometry deals with _______ instead of the triangles of Euclidean Geometry.
Part of Critical Thinking is thinking about more than one solution to a problem.
Learning Geometry will not help my Critical Thinking abilities.
The solution I think best applies to the situation will always give me the correct result.
Sonic the Hedgehog is a result of Applied Geometry?
What Medical Industry would be MOST interested in Geometry?
D. All of the Above
Aeronautics uses Geometry only in airplane design.
What type of Geometry does Aeronautics use the most?
D. None of These
You Answered Incorrectly;
Please Review and Take Quiz Again.
Now You Understand the Importance of 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.