Presentation on theme: "Math Awareness Day College of the Siskiyous April 21, 2010 In collaboration with: COS Mathematics Department Prizes sponsored by: MESA COS Bookstore."— Presentation transcript:
Math Awareness Day College of the Siskiyous April 21, 2010 In collaboration with: COS Mathematics Department Prizes sponsored by: MESA COS Bookstore
Today’s activities 1.Prime Jump! Or Indoor activity 2.Digits of Pi memorization contest 3.Math Charades (if time allows) 4.TRIVIA!
Math Awareness Month is April 2010! http://www.mathaware.org The theme for this year is Math and Sports. PRIME JUMP! A prime number is any number, greater than 1, that is only divisible by 1 and itself. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,… A composite number is divisible by numbers other than 1 and itself 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22,…
Rules for PRIME JUMP 11 contestants compete in the order called. Each contestant takes one turn per round. You may only step on prime numbers. If you step on a composite, you are disqualified! Elimination. After the first round of jumping, primes already used will be crossed off. This will continue each round. The very last person to completely make it through each round without getting disqualified wins a prize!
Indoor game Consecutive Prime Circles Gather into 3 circles at least 11 people per circle The first person chosen by a judge names the number 2. Moving to the left, each person names the next prime number. If you name a composite, you are out! The last person in each group remaining wins a prize! (if you exceed 1,000 everyone left wins a prize!)
An application of Prime numbers! Internet security using credit cards May I borrow a credit card from someone? My credit card number is 1234 5678 9876 5432 Encrypt EACH four digit sequence separately. 1234 5678 9876 5432
Encrypting the credit card # using RSA Encryption Pick 3 prime numbers (13, 43, 59) very specifically chosen (math involved!) Take the first four digits, 1234. Raise this number to the 13 th power (A prime power!) The result of 1234 13 is 15384984961285911141365976368608720 789504
Encrypting the credit card #, cont. The number is approx ~ 1.54x10 40 Take the entire 41 digit number and divide it by 43*59 =2537 (a product of two primes!) The remainder after division takes place is 2391. This is the encrypted message that the other side receives!
Decrypting the message In order for the other party to receive your credit card number, they need the decryption number, d. First, subtract each prime by 1. 43-1 =42, 59-1 = 58. Then, multiply the results together 42*58 = 2436. This will be used to find the decryption number, d, used to decipher the message.
The decryption number To find the decryption number, first look for the smallest number, d, such that when multiplied by the prime 13 and subtracted by 1, is divisible by 2436. In other words, find the smallest number d so that (13d -1)/2436 is a whole number. Want to try? Calculators ready? Prize for the first person to get it! (long pause) Hint: it is between 930 and 940.
Finding the decryption number d = 937 is the decryption number. This is because (13*937)-1 = 12180 and 12180 evenly divides into 2436 (5 times). By knowing the decryption number, the credit card number may be decrypted!
Decrypting the message Without d, the encrypted message and the product of two primes, the other party cannot decrypt your message! To obtain the first four digits of the credit card number: Raise 2391 937 (how big is this?) Divide by 2537 The remainder is 1234, the original number!
Pie and Pi Yum! Dividing the circumference of a circle by its diameter will give you an approximation of pi.
The first 100 digits of PI 3.14159265358979323846264 338327950288419716939937 510582097494459230781640 628620899862803482534211 70679 You have 3 mins,14 secs to memorize as many places!
A mnemonic for memorizing the first 24 digits of Pi. How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics. All of thy geometry, Herr Planck, is fairly hard...: Count the # of letters in each word 3.14159265358979323846264...
Math Charades 3 contestants, 3 teams Each contestant gets a card with a math- related theme on it. Without speaking or spelling out the word. The team will try to guess what the person is acting out. The first team to guess correctly wins their contestant a prize.
Trivia (first person to raise their hand and answer wins a prize!) What type of encryption was used today to secure my credit card number? What are the last names of the people who came up with the RSA Encryption algorithm? What three things do you need to decrypt a message using RSA?
Trivia part 2 What two parts of a circle and in what order do you divide to find the number pi? What is the world record for the number of digits of PI memorized?
Answers What type of encryption was used today to secure my credit card number? –RSA Encryption What are the last names of the people who came up with the RSA Encryption algorithm? –Rivest, Shamir and Adelman What three things do you need to decrypt a message using RSA? –The decryption number, the encrypted message and the product of two primes.
What two parts of a circle and in what order do you divide to find the number PI? –Circumference/Diameter What is the world record for the number of digits of PI memorized? –Lu Chao, China memorized 67,890 digits