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Math Awareness Day College of the Siskiyous April 21, 2010

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. Prime Jump! Or Indoor activity Digits of Pi memorization contest Math Charades (if time allows) TRIVIA!.

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Math Awareness Day College of the Siskiyous April 21, 2010

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  1. Math Awareness DayCollege of the SiskiyousApril 21, 2010 In collaboration with: COS Mathematics Department Prizes sponsored by: MESA COS Bookstore

  2. Today’s activities • Prime Jump! Or Indoor activity • Digits of Pi memorization contest • Math Charades (if time allows) • TRIVIA!

  3. 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,…

  4. 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!

  5. 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!)

  6. 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

  7. 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 13th power (A prime power!) • The result of 123413 is 15384984961285911141365976368608720789504

  8. Encrypting the credit card #, cont. • The number is approx ~ 1.54x1040 • 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!

  9. 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.

  10. 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.

  11. 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!

  12. 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 2391937 (how big is this?) • Divide by 2537 • The remainder is 1234, the original number!

  13. By the way, 2391937 is 5358741658392078027245727162446004805176225273454332287945094936874232325483843766872022479682813780900367785822173123534583434492976979021987887110524163574945487563561529000449827277569356457916027601373461365142219595942600196020883817680941784484871127215814319096536731974026971134406955245583171263740825411410629286534673785486822275331174703708591337472497826977825329769682947831316810879824473089814773278707280853529639107869594589376919650392105787217383870283524511174070630824827236608285246472956528934033521049900084086553003944995733500936766618196839261927690044791255888284490476095831913741372024184153981523821338145148228870639576650480181832609469946228807634796956452473272295204636580699686649425565996274719411966412496220279178123648476833962436499686757436569512212801372723991044495839523702724550840202542259831136814215131277059494638103210012997228537051423647501455501900760296683715573544651416309766302736931374090074185653419696873281035654937820990640382020446872064170360400199814698750995185479059249008549354678496513944889126212390750968889940887810796344139477560200315750206968214088014019785700817412946538623451557423891914415137675482830636633568045501585701485555224363686259614782456108840068618263369828605319481810903759481032695625612850079473077689940180166787241879802781109364448667418447083154009602594607119705622717479194014386036885590900944577148357674618274828605432182540318898381467393149048856066123632449446888276819738714853459701889923427944409162824299500588465113741441600203860176180358761063269481023648081440968537879138320680654825959975261517712805705209157977223006777221884676735126360790518667665060656489971102449170591691704420984409314174372784445041131160206211883150539135708033187096925469577010173744562946432821545045972353847409168618644947064646644314853782405151228150429369770548978572533753529003676695416538852416674907085723664878569616790728268964029697330729992383242822150205943840572740346336846238615868390939635779227623358120503177421668458867687181349295165786415410630853379000329016218791037047776349553912005835244930035511793057263357484894829044914610637491335915852015645196993411561465813949233673263914865181169502563387510736496621026657377697920971275287179821368535798104357166617119075766111637986117586667643617472351715285629986506348409629557224516149777075482288054798106611676974382415534732462477505762180167658693711606471769805030470596501917854830790665531560895692094341956985829017573611226187586524734875061035604774957187833942680417198127010269807472531255632833538308098088961981634013074457252816146330171367390310967704586857082283000285233999395039885797988281706195982516130525307387144840913549902481275759870214785262585572119123609306364290049929894731043409529901468793380672108560494883119771549298856246791263393751895979672207529611287649927805316797922563515320002387982895697099576929322127497474761264108492251008987954128611794633129067022484296232247217951904682383100298053969768788143604661909131888706949765509362420292443477732909130245384886277765595019129264747517359960211615180092340559457545858823979899670499563031

  14. Pie and Pi • Yum! • Dividing the circumference of a circle by its diameter will give you an approximation of pi.

  15. The first 100 digits of PI • 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679 • You have 3 mins,14 secs to memorize as many places!

  16. 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...

  17. 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.

  18. 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?

  19. 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?

  20. 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.

  21. 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

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