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How to Juggle the Proof for Every Theorem an Exploration of the Mathematics Behind Juggling
How to juggle the proof for every theorem An exploration of the mathematics behind juggling Mees Jager 5965802 (0101) 3 0 4 1 2 (1100) (1010) 1 4 4 3 (1001) (0011) 2 0 0 (0110) Supervised by Gil Cavalcanti Contents 1 Abstract 2 2 Preface 4 3 Preliminaries 5 3.1 Conventions and notation . .5 3.2 A mathematical description of juggling . .5 4 Practical problems with mathematical answers 9 4.1 When is a sequence jugglable? . .9 4.2 How many balls? . 13 5 Answers only generate more questions 21 5.1 Changing juggling sequences . 21 5.2 Constructing all sequences with the Permutation Test . 23 5.3 The converse to the average theorem . 25 6 Mathematical problems with mathematical answers 35 6.1 Scramblable and magic sequences . 35 6.2 Orbits . 39 6.3 How many patterns? . 43 6.3.1 Preliminaries and a strategy . 43 6.3.2 Computing N(b; p).................... 47 6.3.3 Filtering out redundancies . 52 7 State diagrams 54 7.1 What are they? . 54 7.2 Grounded or Excited? . 58 7.3 Transitions . 59 7.3.1 The superior approach . 59 7.3.2 There is a preference . 62 7.3.3 Finding transitions using the flattening algorithm . 64 7.3.4 Transitions of minimal length . 69 7.4 Counting states, arrows and patterns . 75 7.5 Prime patterns . 81 1 8 Sometimes we do not find the answers 86 8.1 The converse average theorem . 86 8.2 Magic sequence construction . 87 8.3 finding transitions with flattening algorithm . -
THE BENEFITS of LEARNING to JUGGLE for CHILDREN Written by Dave Finnigan
THE BENEFITS OF LEARNING TO JUGGLE FOR CHILDREN Written by Dave Finnigan Fitness, Motor Skills, Rhythm, Balance, Coordination Benefits . Students can start acquiring pre-juggling skills in pre-school and kindergarten by learning to toss and catch one big, colorful, slow-moving nylon scarf. Once tossing and catching becomes routine, you can use one nylon scarf anywhere that you would normally use a ball or beanbag for most games and many individual challenges. Just think of the scarf as a "ball with training wheels." Scarf juggling and scarf play progresses in a step-by-step manner from one, to two, and on to three. Scarf play and scarf juggling requires big, flowing movements. Children get a great cardio-vascular and pulmonary work-out when they juggle scarves, exercising the big muscles close to the head and close to the heart. They will find scarf juggling to be a great deal of work and lots of fun at the same time. Once they move on to beanbags or other faster moving equipment, they get exercise not only from tossing, but from bending over to pick up errant objects as well. Once a student can juggle continuously, they can "workout" with heavy or bulky objects such as heavyweight beanbags, basketballs, or other items which provide strenuous exercise while they improve focus and dexterity. Because all of this tossing and catching activity can be done to music, you can use different types of music to help children acquire a sense of rhythm and a natural "beat." By working together, students can participate in a group activity requiring concentration and attention to task and reinforcing rhythm. -
Inspiring Mathematical Creativity Through Juggling
Journal of Humanistic Mathematics Volume 10 | Issue 2 July 2020 Inspiring Mathematical Creativity through Juggling Ceire Monahan Montclair State University Mika Munakata Montclair State University Ashwin Vaidya Montclair State University Sean Gandini Follow this and additional works at: https://scholarship.claremont.edu/jhm Part of the Arts and Humanities Commons, and the Mathematics Commons Recommended Citation Monahan, C. Munakata, M. Vaidya, A. and Gandini, S. "Inspiring Mathematical Creativity through Juggling," Journal of Humanistic Mathematics, Volume 10 Issue 2 (July 2020), pages 291-314. DOI: 10.5642/ jhummath.202002.14 . Available at: https://scholarship.claremont.edu/jhm/vol10/iss2/14 ©2020 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. Inspiring Mathematical Creativity Through Juggling Ceire Monahan Department of Mathematical Sciences, Montclair State University, New Jersey, USA -
Book Review: the Mathematics of Juggling, Volume 51, Number 1
Book Review The Mathematics of Juggling Reviewed by Allen Knutson The Mathematics of Juggling • (to avoid considering boundary conditions) The Burkard Polster juggler has been juggling since the infinite past Springer-Verlag, New York, 2003 and will continue into the infinite future. 226 pages, $39.95 • The throws come one per second, with right ISBN 0-387-95513-5 throws at even times and left throws at odd times (this can be ensured by reparametrizing Around 1985 three groups of jugglers (in Santa the time coordinate). Cruz, California; in Pasadena, California; and in More notable, though, is the assumption about Cambridge, England) independently created the what one actually wants to record: same notational system for juggling patterns. These • The only information kept about the ball thrown ∈ Z numerical descriptions have been well publicized at time n is when it is next thrown, at time in the juggling world under the name “siteswaps” f (n). (and, even so, continue to be rediscovered by new- In particular, this assumption loses any extra de- comers). tail about the throw like “under the leg”, “with a triple spin” (if the objects juggled are pins rather As we will see shortly upon presentation of the than balls), “while telling joke #1729”, etc. But it basic definitions, a rather simple list of restric- suggests a very nice mathematical theory of cer- tions leads easily to a unique notational system. tain functions f : Z → Z: More surprising is the near-simultaneity of the dis- 1. The function f should be one-to-one, since we covery! The best explanation of this seems to be do not want two balls landing at the same time. -
The Beginner's Guide to Circus and Street Theatre
The Beginner’s Guide to Circus and Street Theatre www.premierecircus.com Circus Terms Aerial: acts which take place on apparatus which hang from above, such as silks, trapeze, Spanish web, corde lisse, and aerial hoop. Trapeze- An aerial apparatus with a bar, Silks or Tissu- The artist suspended by ropes. Our climbs, wraps, rotates and double static trapeze acts drops within a piece of involve two performers on fabric that is draped from the one trapeze, in which the ceiling, exhibiting pure they perform a wide strength and grace with a range of movements good measure of dramatic including balances, drops, twists and falls. hangs and strength and flexibility manoeuvres on the trapeze bar and in the ropes supporting the trapeze. Spanish web/ Web- An aerialist is suspended high above on Corde Lisse- Literally a single rope, meaning “Smooth Rope”, while spinning Corde Lisse is a single at high speed length of rope hanging from ankle or from above, which the wrist. This aerialist wraps around extreme act is their body to hang, drop dynamic and and slide. mesmerising. The rope is spun by another person, who remains on the ground holding the bottom of the rope. Rigging- A system for hanging aerial equipment. REMEMBER Aerial Hoop- An elegant you will need a strong fixed aerial display where the point (minimum ½ ton safe performer twists weight bearing load per rigging themselves in, on, under point) for aerial artists to rig from and around a steel hoop if they are performing indoors: or ring suspended from the height varies according to the ceiling, usually about apparatus. -
Happy Birthday!
THE THURSDAY, APRIL 1, 2021 Quote of the Day “That’s what I love about dance. It makes you happy, fully happy.” Although quite popular since the ~ Debbie Reynolds 19th century, the day is not a public holiday in any country (no kidding). Happy Birthday! 1998 – Burger King published a full-page advertisement in USA Debbie Reynolds (1932–2016) was Today introducing the “Left-Handed a mega-talented American actress, Whopper.” All the condiments singer, and dancer. The acclaimed were rotated 180 degrees for the entertainer was first noticed at a benefit of left-handed customers. beauty pageant in 1948. Reynolds Thousands of customers requested was soon making movies and the burger. earned a nomination for a Golden Globe Award for Most Promising 2005 – A zoo in Tokyo announced Newcomer. She became a major force that it had discovered a remarkable in Hollywood musicals, including new species: a giant penguin called Singin’ In the Rain, Bundle of Joy, the Tonosama (Lord) penguin. With and The Unsinkable Molly Brown. much fanfare, the bird was revealed In 1969, The Debbie Reynolds Show to the public. As the cameras rolled, debuted on TV. The the other penguins lifted their beaks iconic star continued and gazed up at the purported Lord, to perform in film, but then walked away disinterested theater, and TV well when he took off his penguin mask into her 80s. Her and revealed himself to be the daughter was actress zoo director. Carrie Fisher. ©ActivityConnection.com – The Daily Chronicles (CAN) HURSDAY PRIL T , A 1, 2021 Today is April Fools’ Day, also known as April fish day in some parts of Europe. -
JUGGLING in the U.S.S.R. in November 1975, I Took a One Week Tour to Leningrad and Ring Cascade Using a "Holster” at Each Side
Volume 28. No. 3 March 1976 INTERNATIONAL JUGGLERS ASSOCIATION from Roger Dol/arhide JUGGLING IN THE U.S.S.R. In November 1975, I took a one week tour to Leningrad and ring cascade using a "holster” at each side. He twice pretended Moscow, Russia. I wasfortunate to see a number of jugglers while to accidentally miss the catch of all 9 down over his head before I was there. doing it perfectly to rousing applause and an encore bow. At the Leningrad Circus a man approximately 45 years old did Also on the show was a lady juggler who did a short routine an act which wasn’t terribly exciting, though his juggling was spinning 15-inch square glass sheets. She finished by spinning pretty good. He did a routine with 5, 4, 3 sticks including one on a stick balanced on her forehead and one on each hand showering the 5. He also balanced a pole with a tray of glassware simultaneously. Then, she did the routine of balancing a tray of on his head and juggled 4 metaf plates. For a finish, he cqnter- glassware on a sword balanced point to point on a dagger in her spun a heavy-looking round wooden table upside-down on a 10- mouth and climbing a swaying ladder ala Rosana and others. foot sectioned pole balanced on his forehead, then knocked the Finally, there were two excellent juggling acts as part of a really pole away and caught the table still spinning on a short pole held great music and variety floor show at the Arabat Restaurant in in his hands. -
What's Happening at the IJA ?
THE INTERNATIONAL JUGGLERS’ ASSOCIATION October 2007 IJA e-newsletter editor: Don Lewis (email: [email protected]) Renew at http://www.juggle.org/renew What’s Happening at the IJA ? In This Issue: 2008 Lexington IJA Festival Help Wanted Have You Moved, or Gotten a New Email Address? Treasury Remember, the only way to ensure that you don't miss a World Juggling Day single issue of JUGGLE magazine is to give us your new Marketing the IJA address. The USPS will generally not forward JUGGLE Joggling Record magazine. Insurance To update your mailing address, email, or phone, please Regional Festivals send email to [email protected] or call TurboFest - Quebec City 415-596-3307 or write to: IJA, PO Box 7307, Austin, TX 78713-7307 USA. World Circus Year 2008 IJA Festival, Lexington, Kentucky The Hyatt is connected to the convention center. The convention center has a food court and shops and they are Lexington Notes by Richard Kennison open on a daily basis. There is a vibrant downtown area right Everyone, around the convention center. I just spent two days in Lexington, KY. I am very thrilled to tell The convention center contact person, the hotel contact person you that I think it is a wonderful site. I will not go into long and the theatre contact person are all professional and excited details here but: that we are coming. Bond Jacobs—the visitors bureau contact You can park your car (for free if you stay the the Hyatt) and person is an asset and will go the extra mile for us. -
Fargo Convention Well Worth the Journey
August 1980 Vol. 32 No. 5 Membership—1,200 1981 Convention Site—Cleveland, OH, Case Western Reserve University Fargo convention well worth the journey In anticipation of sharing talent and watching jugglers in the crowded party room witti the promise Benefit shows for crowds at the NDSU student some of the best jugglers in North America at work, of greater support if the IJA would return to Fargo union, the Red River Mall, a Shrine club and a 475 people trekked through mid July heat to Faigo, nextyear. Reaction was not positive, and conven- nursing home demonstrated IJA’s appreciation ND, site of the 33rd IJA annual convention, tioneers later voted Cleveland. OH, as the 1981 for the hospitality, There, close by the geographical center of the site (see page 6). The convention ran smoothly, and largely on time. continent, they witnessed the basics—like 3-ball High-rise lodging contained two-story foyer areas and 5-club cascades—and the outer limits of jug that were ideal for juggling. The university food gling skill, as demonstrated by Michael Kass’s prize service fed 165 jugglers three times day, and cater winning performance of club kick-ups. The same ed a pleasant outdcxar "buffalo" barbeque at Troll- lure of communion with fellow jugglers has drawn wood Park on Saturday. this group together annually since 1947, when The Saturday morning parade included many the founding fathers formed the group during a other area groups, and was aired by NBC news convention of the international Brotherhood of on a late-night broadcast. -
Vpliv Gibalnih Sposobnosti Na Žongliranje Diplomsko Delo
UNIVERZA V LJUBLJANI FAKULTETA ZA ŠPORT Športna vzgoja Vpliv gibalnih sposobnosti na žongliranje Diplomsko delo MENTOR: prof. dr. Ivan Čuk SOMENTORICA: doc. dr. Maja Bučar Pajek RECEZENTKA: prof. dr. Maja Pori AVTOR: Blaž Slanič Ljubljana, 2015 ZAHVALA Zahvaljujem se vsem žonglerjem, brez njih diplomskega dela ne bi mogel izpeljati. Zahvala gre tudi mentorju, profesorju dr. Ivanu Čuku, ki mi je pomagal pri sami izvedbi diplomskega dela. Hvala partnerki in staršem, ki me pri mojih žonglersko-akrobatskih podvigih podpirate in mi stojite ob strani. HVALA. Ključne besede: žongliranje, gibalne sposobnosti, učinkovitost Vpliv gibalnih sposobnosti na žongliranje IZVLEČEK: Ker je žongliranje v Sloveniji zelo malo poznano, smo naredili raziskavo o vplivu gibalnih sposobnosti na unčikovitost v žongliranju. V raziskavi smo testirali gibalne sposobnosti slovenskih žonglerjev vseh starosti. Raziskava je vsebovala teste hitrosti, moči, ravnotežja, preciznosti, reakcijskega časa in ritma. Vse teste smo izvedli z levo in desno roko. Pogoj za sodelovanje na raziskavi je bil, da posameznik zna žonglirati s petimi žonglerskimi žogicami. Sodelovalo nas je 16 žonglerjev, starih med 13 in 40 let, in sicer 15 moških in 1 ženska. Na podlagi rezultatov smo ugotavljali, katere od gibalnih sposobnosti so tiste ključne, ki pripomorejo k lažjemu in bolj kontroliranemu žonglerskemu udejstvovanju. Podatki so bili obdelani v programu Excel 2010 in SPSS 16.0. Iz naših rezultatov je razvidno, da imata na učinkovitost v žongliranju največji vpliv bobnanje leva roka (ritem in tempo leve roke) in starost posameznika. Keywords: Juggling, motor skills, efficiency Effects of motor skills on juggling Because of the lesser known nature of jugging in Slovenia, we made our research on the effects of motor skills on it. -
Class of 1965 50Th Reunion
CLASS OF 1965 50TH REUNION BENNINGTON COLLEGE Class of 1965 Abby Goldstein Arato* June Caudle Davenport Anna Coffey Harrington Catherine Posselt Bachrach Margo Baumgarten Davis Sandol Sturges Harsch Cynthia Rodriguez Badendyck Michele DeAngelis Joann Hirschorn Harte Isabella Holden Bates Liuda Dovydenas Sophia Healy Helen Eggleston Bellas Marilyn Kirshner Draper Marcia Heiman Deborah Kasin Benz Polly Burr Drinkwater Hope Norris Hendrickson Roberta Elzey Berke Bonnie Dyer-Bennet Suzanne Robertson Henroid Jill (Elizabeth) Underwood Diane Globus Edington Carol Hickler Bertrand* Wendy Erdman-Surlea Judith Henning Hoopes* Stephen Bick Timothy Caroline Tupling Evans Carla Otten Hosford Roberta Robbins Bickford Rima Gitlin Faber Inez Ingle Deborah Rubin Bluestein Joy Bacon Friedman Carole Irby Ruth Jacobs Boody Lisa (Elizabeth) Gallatin Nina Levin Jalladeau Elizabeth Boulware* Ehrenkranz Stephanie Stouffer Kahn Renee Engel Bowen* Alice Ruby Germond Lorna (Miriam) Katz-Lawson Linda Bratton Judith Hyde Gessel Jan Tupper Kearney Mary Okie Brown Lynne Coleman Gevirtz Mary Kelley Patsy Burns* Barbara Glasser Cynthia Keyworth Charles Caffall* Martha Hollins Gold* Wendy Slote Kleinbaum Donna Maxfield Chimera Joan Golden-Alexis Anne Boyd Kraig Moss Cohen Sheila Diamond Goodwin Edith Anderson Kraysler Jane McCormick Cowgill Susan Hadary Marjorie La Rowe Susan Crile Bay (Elizabeth) Hallowell Barbara Kent Lawrence Tina Croll Lynne Tishman Handler Stephanie LeVanda Lipsky 50TH REUNION CLASS OF 1965 1 Eliza Wood Livingston Deborah Rankin* Derwin Stevens* Isabella Holden Bates Caryn Levy Magid Tonia Noell Roberts Annette Adams Stuart 2 Masconomo Street Nancy Marshall Rosalind Robinson Joyce Sunila Manchester, MA 01944 978-526-1443 Carol Lee Metzger Lois Banulis Rogers Maria Taranto [email protected] Melissa Saltman Meyer* Ruth Grunzweig Roth Susan Tarlov I had heard about Bennington all my life, as my mother was in the third Dorothy Minshall Miller Gail Mayer Rubino Meredith Leavitt Teare* graduating class. -
In-Jest-Study-Guide
with Nels Ross “The Inspirational Oddball” . Study Guide ABOUT THE PRESENTER Nels Ross is an acclaimed performer and speaker who has won the hearts of international audiences. Applying his diverse background in performing arts and education, Nels works solo and with others to present school assemblies and programs which blend physical theater, variety arts, humor, and inspiration… All “in jest,” or in fun! ABOUT THE PROGRAM In Jest school assemblies and programs are based on the underlying principle that every person has value. Whether highlighting character, healthy choices, science & math, reading, or another theme, Nels employs physical theater and participation to engage the audience, juggling and other variety arts to teach the concepts, and humor to make it both fun and memorable. GOALS AND OBJECTIVES This program will enhance awareness and appreciation of physical theater and variety arts. In addition, the activities below provide connections to learning standards and the chosen theme. (What theme? Ask your artsineducation or assembly coordinator which specific program is coming to your school, and see InJest.com/schoolassemblyprograms for the latest description.) GETTING READY FOR THE PROGRAM ● Arrange for a clean, well lit SPACE, adjusting lights in advance as needed. Nels brings his own sound system, and requests ACCESS 4560 minutes before & after for set up & take down. ● Make announcements the day before to remind students and staff. For example: “Tomorrow we will have an exciting program with Nels Ross from In Jest. Be prepared to enjoy humor, juggling, and stunts in this uplifting celebration!” ● Discuss things which students might see and terms which they might not know: Physical Theater..