T HE 8 “P” S OF M ATH Created by: Rachel Siepelinga Pi Pie Picture From: loneliest-numberhttp://deadspin.com/368152/pi-is-the- loneliest-number

T HE N INE P’ S OF M ATH 1. Pascal’s Triangle 2. Pascal’s Law 3. Properties of Real Numbers 4. Pi 5. Pythagorean Theorem 6. Prime Numbers 7. Perfect Numbers 8. Perfect Squares P

PIPI Pi is an irrational number, it is also classified as real. You can use Pi for, circumference, diameter, and to challenge people. Here are some cool pictures about pi… Neon Pi picture from:

What is PI Squared? PI Squared is What is PI Cubed? PI Cubed is Pi Squared picture from: Pi Cubed picture from:

W HAT I S T HE S QUARE R OOT O F P I It is, … Mystical Pi Picture from: otofpi.com/ otofpi.com/

P I V IDEO F ROM B RAIN P OP Brian Pop – Math picture from: Brain Pop logo picture from: Moby picture from: HTTP :// WWW. BRAINPOP. COM // MATH / NUMBERSANDOPERATIONS / PI / FYI /

FIND YOUR BIRTHDAY IN PI Birthday Pi Image From: hettbooks.com hettbooks.com

C OOL F ACTS A BOUT P I In 2002, a Japanese scientist found 1.24 trillion digits of pi using a powerful computer called the Hitachi SR 8000, breaking all previous records The first 144 digits of pi add up to 666 (which many scholars say is “the mark of the Beast”). And 144 = (6+6) x (6+6) We can never truly measure the circumference or the area of a circle because we can never truly know the value of pi. Pi is an irrational number, meaning its digits go on forever in a seemingly random sequence. The symbol for pi (π) has been used regularly in its mathematical sense only for the past 250 years. We can never truly measure the circumference or the area of a circle because we can never truly know the value of pi. Pi is an irrational number, meaning its digits go on forever in a seemingly random sequence. In the Greek alphabet, π ( piwas ) is the sixteenth letter. In the English alphabet, p is also the sixteenth letter. Pi has been studied by the human race for almost 4,000 years. By 2000 B.C., Babylonians established the constant circle ratio as 3-1/8 or The ancient Egyptians arrived at a slightly different value of 3-1/7 or The first million decimal places of pi consist of 99,959 zeros, 99,758 1s, 100,026 2s, 100,229 3s, 100,230 4s, 100,359 5s, 99,548 6s, 99,800 7s, 99,985 8s, and 100,106 9s. The first six digits of pi (314159) appear in order at least six times among the first 10 million decimal places of pi. In the Star Trek episode “Wolf in the Fold,” Spock foils the evil computer by commanding it to “compute to last digit the value of pi.” Pi Facts from: ry.com/2009/07/03_pi.ht ml ry.com/2009/07/03_pi.ht ml

H OW C ROP C IRCLES C ONNECT WITH P I A mysterious 2008 crop circle in Britain shows a coded image representing the first 9 digits of pi. This only works if you round the tenth digit of Pi. Pi Crop Circle Picture from: depicts-pi/ depicts-pi/

W HO C REATED P I ? Archimedes and the Greeks. Born in Syracuse and educated in Alexandria, Archimedes was one of the most important mathematicians and inventors of the ancient world. He is best known for his phrase "eureka" (I have found it). The story goes that king Hieron of Syracusae suspected that the crown he had ordered from a goldsmith was not of pure gold. He then asked the genius Archimedes to find a way to measure the crown. The solution came to him when he stepped into his bath and saw the water overflowing. By measuring the water that runs over when an object is put into it, one can measure the objects weight, he concluded. According to the legend, Archimedes ran naked through the streets shouting the famous phrase. Archimedes also invented the method to measure the surface and volume of a globe, and made the final determination of pi. He defined the principle of the lever, and in Egypt he invented the hydraulic screw for raising the water from a lower to a higher level. When the Romans conquered Sicily, he gave them many inventions used for the defense of Syracuse, for example the catapult and maybe a system of mirrors focusing the sunrays on boats and igniting them. Archimedes was killed by a Roman soldier who was offended when the scientist asked him not to disturb the diagrams he was drawing in the sand. Surviving works are Floating Bodies, The Sand Reckoner, Measurement of the Circle, Spirals and Sphere and Cylinder. Archimedes Information found from: ncient/archimedes.htm ncient/archimedes.htm * Even Though Someone created Pi, no one knows the true value of Pi.*

P RIME N UMBERS Prime Numbers are numbers that are only divisible by 1 and itself. So 3 would be prime, because you can only divide it by 1 and 3. However 4 would not be prime because it can be divided by, 1, 2, and 4. The number 1 is neither prime nor composite. Two is the only even number that is prime. All prime numbers are odd with the exception of 2. However not all odd numbers are prime. Prime Numbers are circled.

P ASCAL ’ S L AW Pascal's law states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container. For example, If you increase the pressure in the bottom of the tank. Every other part of the tank will also increase in pressure. Not just where you increased the pressure.

P ERFECT N UMBERS A perfect number is a positive integer that is the sum of its divisors. So 6 is a perfect number because its divisors. (1, 2, and 3) = 6 The next one is is a perfect number because its divisors. (1, 2, 4, 7, 14) = 28 The next perfect Number is, 496 and then These four numbers were the only ones known to early Greek mathematics.

P ERFECT S QUARES Any number that is the square of a rational number. For example, 0, 1, 4, 9, 16, 25, etc. are all perfect squares. You can tell if a number is a perfect square if the number when you find the square root is an integer. For Example: 25 is a perfect square because the √25 is 5.

P ROPERTIES OF R EAL N UMBERS 0 is a real number. 1 is a real number. If two real numbers are multiplied or added their sum or product will be a real number. A real number other than 0, its reciprocal will also be a real number. If a number is real. Its opposite is also real. All real numbers are complex numbers. All imaginary numbers, i. i * i = -1 3i * 3i = -1 Given two different real numbers x and y. Either x > y or y > x but never both. ex. x = 3 and y = 4 y > x but x is not greater that y. Given three different real numbers x, y, and z. If x > y, y > z, then x > z. ex. x = 5, y = 4, and z = 3 x > y, y > z, then x > z. BECAUSE 5 > 4, 4 > 3, then 5 > 3 There is no real number x, that x > x. ex. x = 3, so x is not > than x, because they are equal to. There is no complete set of real numbers, because the numbers just don’t stop. There is not a smallest number, because numbers go “to infinity and beyond,” – Buzz Lightyear. ex. -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6 Because you can go past 6 in either direction.

P YTHAGOREAN T HEOREM The formula is a² + b² = c² It must be a right triangle. c must be the hypotenuse. a and b must be the two sides. Everything must be squared. Example – There is a right triangle, with sides a, b, and c. a = 3, b = 4, c = ? 3² + 4² = c² = c² 25 = c² √25 = √c² 5 = c

P YTHAGOREAN T HEOREM E XAMPLE Pick a problem. 3 4 x Easy 9 12 x Mediumish 7 10 x Hardish

P YTHAGOREAN T HEOREM E ASY P ROBLEM a² + b² = c² 3² + 4² = c² = c² 25 = c² √25 = √c² 5 = c Write Formula Fill in the variables that you know. Simplify the exponents. Add them. Find the square root. 5 = c Tap the magical box, WHEN I TELL YOU TO!!!!!!!!!!!!

P YTHAGOREAN T HEOREM M EDIUMISH P ROBLEM a² + b² = c² 9² + 12² = c² = c² 225 = c² √225 = √c² 15 = c Write Formula Fill in the variables that you know. Simplify the exponents. Add them. Find the square root. 15 = c Tap the magical box, WHEN I TELL YOU TO!!!!!!!!!!!!

P YTHAGOREAN T HEOREM H ARDISH a² + b² = c² 7² + 10² = c² = c² 149 = c² √149 = √c² 12.2 = c Write Formula Fill in the variables that you know. Simplify the exponents. Add them. Find the square root = c Tap the magical box, WHEN I TELL YOU TO!!!!!!!!!!!!

W ORK C ITED Work Cited 1.Morris, Stephanie. “The Pythagorean Theorem.” The University of Georgia. November 11, <jwilson.coe.uga.edu/emt669/students.folders/m orris.stephanie/emt.669/essay.1/pythagorean.ht ml