AUGUST 2013 HISTORY OF GEOMETRY THEOREMS & POSTULATES

DO NOW In a mini-paragraph (3-5 sentences) answer the following questions: What do you already know about Geometry? What do you think you will learn in Geometry this year? Be as specific as possible and include any vocabulary that you think will be important or any examples of Geometry that you are already familiar with.

By the end of the day today, IWBAT… Identify the purpose and history of Geometry Why it matters in LIFE : Geometry has a long history and has impacted many, many civilizations over time. It continues to be used every day. Why it matters in THIS CLASS : It is important to understand the history of our subject before we begin our work this year.

Geometry was created out of necessity by the ancient Egyptians Flooding of the Nile River would cause some of the tenants of the Pharaoh’s land to lose crops, so the tenants would refuse to pay “rent” for the flooded land. The Egyptians then figured out how to measure the area to adjust the “rent”. “MATHEMAGYPTIANS”

INDUS VALLEY ARCHITECTS Manufactured bricks whose dimensions were in the proportion 4:2:1, to make a stable brick. They mass-produced weights in regular geometrical shapes, which included hexahedra, barrels, cones, and cylinders.

Kept daily records of the rising and setting of stars, the motion of the planets, and the solar and lunar eclipses. These measurements required them to understand the angles stars made with each other and the earth Pythagoras, who is credited with the Pythagorean Theorem, was also from Babylon BABYLONIAN ASTRONOMERS

IN COMES EUCLID… Euclid is known as the father of Geometry He wrote a book called The Elements which is based on 5 Postulates

ARAB GEOMETRY Art, decoration Repetitions of basic motif Mathematical because not all shapes can cover a plane surface through repetition Symmetry

ADDING COMPLEXITY There are now other kinds of Geometry that deal with curved surfaces, hyperbolic surfaces (like a wave or horse saddle), and even something called taxi cab geometry.

POSTULATES A point of reasoning that is accepted as true without proof. A starting point for higher level understanding Common Sense Postulates are PROVEN! “Things which are equal to the same thing are also equal to one another.”

THEOREMS A statement that requires proof Proof can come from other theorems, postulates, or definitions. Still true, just need to be proven Well known example: The Pythagorean Theorem

POSTULATE OR THEOREM? The sky is blue

POSTULATE OR THEOREM? The whole is greater than the part.

POSTULATE OR THEOREM? Hand sanitizer keeps you safe from germs

POSTULATE OR THEOREM? Dominos Pizza is the most popular pizza

POSTULATE OR THEOREM? There are 4 quarters in a football game

CHECK YOUR UNDERSTANDING Write down one theorem and postulate of your own. Be prepared to share with a partner. These may be related to Geometry, math, or your own interests and life.

INDEPENDENT PRACTICE Determine if the following statements are theorems or postulates and include a justification using words or numeric examples: 1. A baseball can be thrown at speeds greater than 100 mph 2. Any number greater than 100 can be divided by 5 3. There are 365 days in a year 4. A square has four sides 5. Glass will break if you drop it on concrete 6. Every integer greater than 1 is either prime or the product of prime numbers

What are some reasons why some truths are accepted while others need proof?

PRACTICE MAKES PERMANENT! One-Step Equations Solve means to isolate x, or get it by itself Use opposite operations to undo what is there 1.15 = y – = y X = y = 10

PRACTICE MAKES PERMANENT! Multi-Step Equations Solve means to isolate x, or get it by itself Use opposite operations to undo what is there Start with operations farthest away from x

Multi-Step Equations – start the farthest from x

6(2x + 1) = x + 4 = 3x TRY IT OUT!

LIFE’S WORK 1.Add the words theorem and postulate to your glossary 2.Complete solving equations from Independent Practice