Transcript Math Awareness Day - College of the Siskiyous
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 (
13
d
-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.
13 ( 937 ) 2436 1
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!
By the way,
2391
937
is
53587416583920780272457271624460048051762252734543322879450949368742323254838437668720224796828137809003677858 22173123534583434492976979021987887110524163574945487563561529000449827277569356457916027601373461365142219595 94260019602088381768094178448487112721581431909653673197402697113440695524558317126374082541141062928653467378 54868222753311747037085913374724978269778253297696829478313168108798244730898147732787072808535296391078695945 89376919650392105787217383870283524511174070630824827236608285246472956528934033521049900084086553003944995733 50093676661819683926192769004479125588828449047609583191374137202418415398152382133814514822887063957665048018 18326094699462288076347969564524732722952046365806996866494255659962747194119664124962202791781236484768339624 36499686757436569512212801372723991044495839523702724550840202542259831136814215131277059494638103210012997228 53705142364750145550190076029668371557354465141630976630273693137409007418565341969687328103565493782099064038 20204468720641703604001998146987509951854790592490085493546784965139448891262123907509688899408878107963441394 77560200315750206968214088014019785700817412946538623451557423891914415137675482830636633568045501585701485555 22436368625961478245610884006861826336982860531948181090375948103269562561285007947307768994018016678724187980 27811093644486674184470831540096025946071197056227174791940143860368855909009445771483576746182748286054321825 40318898381467393149048856066123632449446888276819738714853459701889923427944409162824299500588465113741441600 20386017618035876106326948102364808144096853787913832068065482595997526151771280570520915797722300677722188467 67351263607905186676650606564899711024491705916917044209844093141743727844450411311602062118831505391357080331 87096925469577010173744562946432821545045972353847409168618644947064646644314853782405151228150429369770548978 57253375352900367669541653885241667490708572366487856961679072826896402969733072999238324282215020594384057274 03463368462386158683909396357792276233581205031774216684588676871813492951657864154106308533790003290162187910 37047776349553912005835244930035511793057263357484894829044914610637491335915852015645196993411561465813949233 67326391486518116950256338751073649662102665737769792097127528717982136853579810435716661711907576611163798611 75866676436174723517152856299865063484096295572245161497770754822880547981066116769743824155347324624775057621 80167658693711606471769805030470596501917854830790665531560895692094341956985829017573611226187586524734875061 03560477495718783394268041719812701026980747253125563283353830809808896198163401307445725281614633017136739031 09677045868570822830002852339993950398857979882817061959825161305253073871448409135499024812757598702147852625 85572119123609306364290049929894731043409529901468793380672108560494883119771549298856246791263393751895979672 20752961128764992780531679792256351532000238798289569709957692932212749747476126410849225100898795412861179463 31290670224842962322472179519046823831002980539697687881436046619091318887069497655093624202924434777329091302 45384886277765595019129264747517359960211615180092340559457545858823979899670499563031
Pie and Pi
• Yum!
• Dividing the circumference of a circle by its diameter will give you an approximation of pi.
circumfere nce diameter
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