# The Mathematics of Juggling

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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 .
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• Inspiring Mathematical Creativity Through Juggling
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• 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.
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• TERRAIN INTELLIGENCE Ifope~}M' Oy QUARTERMASTER SCHOOL Lubflar
MHI tI"Copy ? ·_aI i-,I C'opy 31 77 /; DEPARTMENT OF 'THE ARMY FIELD MANUAL TERRAIN INTELLIGENCE IfOPE~}m' Oy QUARTERMASTER SCHOOL LUBflAR. U.S. ARMY QUA. TZ. MSIR SCL, FORT LEE, VA. 22YOlS ,O.ISTx L.at. : , .S, HEAD QU ARTER S, DEPARTMENT OF T HE ARMY OCTOBER 1967 *FM 30-10 FIELD MANUAL HEADQUARTERS DEPARTMENT OF THE ARMY No. 30-10 I WASHINGTON, D.C., 24 October 1967 TERRAIN INTELLIGENCE CHAPTER 1. INTRODUCTION ..........................-- 1-3 2. CONCEPTS AND RESPONSIBILITIES Section I. Nature of terrain intelligence _____.______ .__. 4-7 II. Responsibilities -. ------------------- 8-11 CHAPTER 3. PRODUCTION OF TERRAIN INTELLIGENCE Section I. Intelligence cycle __ …...__…____-----__-- 12-16 II. Sources and agencies ….................... .--- 17-23 CHAPTER 4. WEATHER AND CLIMATE Section I. Weather ..................................... 24-39 II. Climate -.................................. 40-47 III. Operations in extreme climates _................. 48-50 CHAPTER 5. NATURAL TERRAIN FEATURES Section I. Significance .................................. 51, 52 II. Landforms __________ _------------- ------- 53-61 Drainage............................. 62-69 IV. Nearshore oceanography ................. 70-75 V. Surface materials ............................ 76-81 VI. Vegetation ................................... 82-91 CHAPTER 6. MANMADE TERRAIN FEATURES Section I. Significance -.............................. 92, 93 II. Lines of communication ….................... 94-103 III. Petroleum and natural gas ____. _._______.___ 104-108 IV. Mines, quarries, and pits ….................... 109-112 V. Airfields ----------------------------- 113-115 VI. Water terminals _______…-------- ----------- 116-118 VII. Hydraulic structures -........................ 119-121 VIII. Urban areas and buildings ................... 122-128 IX. Nonurban areas ___ _--------------------- 129-131 CHAPTER 7. MILITARY ASPECTS OF THE TERRAIN Section I. Military use of terrain _....._________._____._ 132-139 Ii. Special operations ......................... 140, 141 III.
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• 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.
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• Comprehensive Security Analyses of a Toys-To-Life Game and Possible Countermeasures Master Thesis - July 2016
Comprehensive security analyses of a toys-to-life game and possible countermeasures Master thesis - July 2016 Author Kevin Valk Radboud University [email protected] Supervisor Supervisor Second reader Robert Leyland Lejla Batina Eric Poll Radboud University Radboud University [email protected] [email protected] Abstract This thesis aims at modeling important attacks on a toys-to-life game using attack-defense trees. Using these trees, diﬀerent practical attacks are executed to verify the current coun- termeasures and ﬁnd possible new exploits. One critical exploit led to a binary dump of the ﬁrmware, which made it possible to reverse the key derivation algorithm. This led to breaking the security layer that protected the toys. With the key derivation algorithm known, toys could be forged for under a dollar and made it possible to search for unreleased toys and variants. Given the possible attacks, numerous countermeasures are presented to protect games against these attacks and improve general security. The foremost countermeasure is the addi- tion of digital signatures to the toys. This countermeasure makes it infeasible to forge toys. However, this does not stop 1-on-1 clones, but concepts are explored to protect against 1-on-1 clones in the future using Physical Unclonable Function (PUF). 1 Contents 1 Introduction 4 2 Background 5 2.1 Attack Trees.......................................5 2.1.1 Basic attack-defense trees............................5 2.1.2 Quantitative analysis...............................6 2.2 Public-key cryptography.................................6 2.3 Near Field Communication...............................7 2.3.1 MIFARE Classic.................................7 2.3.2 MIFARE Classic knockoﬀ tags.........................8 3 Threat model 10 4 Attacks 14 4.1 Proxmark III......................................
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• The University of Chicago Sentient Atmospheres A
THE UNIVERSITY OF CHICAGO SENTIENT ATMOSPHERES A DISSERTATION SUBMITTED TO THE FACULTY OF THE DIVISION OF THE HUMANITIES IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF ENGLISH LANGUAGE AND LITERATURE BY JEFFREY HAMILTON BOGGS CHICAGO, ILLINOIS JUNE 2016 Copyright © 2016 by Jeffrey Hamilton Boggs All rights reserved Table of Contents ACKNOWLEDGEMENTS ........................................................................................................... iv INTRODUCTION .......................................................................................................................... 1 I. ATMOSPHERE IN LATE LATE JAMES ............................................................................... 21 II. “WE HAD THE AIR”: THE ATMOSPHERIC FORM OF THE VIETNAM WAR .............. 48 III. THIS IS AIR: THE ATMOSPHERIC POLITICS OF DAVID FOSTER WALLACE ......... 87 IV. NARRATING THE ANTHROPOCENE: THE ATMOSPHERIC COMEDY ................... 120 CODA: PLANETARY AIR ....................................................................................................... 150 BIBLIOGRAPHY ....................................................................................................................... 160 iii ACKNOWLEDGEMENTS I am grateful to the members of my dissertation committee for their unwavering support throughout the course of my academic progress. Bill Brown embodies the very best of the intellectual culture of the University of Chicago. He combines a big mind with a highly refined sensibility, exquisite taste
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• Understanding Siteswap Juggling Patterns a Guide for the Perplexed by Greg Phillips, [email protected]
Understanding Siteswap Juggling Patterns A guide for the perplexed by Greg Phillips, [email protected] Core rules (for all patterns) Synchronous siteswap (simultaneous throws) C1 We imagine a metronome ticking at some constant rate. Some juggling patterns involve both hands throwing at the Each tick is called a “beat.” same time. We describe these using synchronous siteswap. C2 We indicate each thrown object by a number that tells us how many beats later that object must be back in a hand S1 The right and left hands throw at the same time (which and ready to re-throw. counts as two throws) on every second beat. We group C3 We indicate a sequence of throws by a string of numbers the simultaneous throws in parentheses and separate the (plus punctuation and the letter x). We imagine these hands with commas. strings repeat indefinitely, making 531 equivalent to S2 We indicate throws that cross from hand to hand with an …531531531… So are 315 and 153 — can you see x (for ‘xing’). why? C4 The sum of all throw numbers in a siteswap string divided Rules C2 and S1 taken together demand that there be only by the number of throws in the string gives the number of even numbers in valid synchronous siteswaps. Can you see objects in the pattern. This must always be a whole why? The x notation of rule S2 is required to distinguish number. 531 is a three-ball pattern, since (5+3+1)/3 patterns like (4,4) (synchronous fountain) from (4x,4x) equals three; however, 532 cannot be juggled since (synchronous crossing).
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• WORKSHOP SCHEDULE IJA Festival, Sparks, Nevada, July 26 - August 1, 2010
WORKSHOP SCHEDULE IJA Festival, Sparks, Nevada, July 26 - August 1, 2010. For updates, see http://www.juggle.org/festival Tuesday, July 27 8:00am Joggling Competition 9:00am IJA College Credit Meeting -- Don Lewis 10:00am 3 Club Tricks -- Don Lewis (BEG) 10:00am Siteswap 101 -- Chase Martin (and Jordan Campbell) 10:00am Stretching and Increasing Your Flexibility -- Corey White 11:00am Blind Thows & Catches -- Thom Wall 11:00am Five Balls the Easy Way -- Dave Finnigan 11:00am Jammed Knot Knotting Jam -- John Spinoza 12:00pm 3/4 Ball Freezes -- Matt Hall 12:00pm Basic Hoop Juggling Technique -- Carter Brown 12:00pm Poi -- Sam Malcolm (BEG) 1:00pm Special Workshop -- Kris Kremo 1:00pm 180's/360's/720's -- Josh Horton & Doug Sayers 1:00pm Club Passing Routine -- Cindy Hamilton 1:00pm Tennis Ball/Can Breakout -- Dan Holzman 2:00pm Intro to Ball Spinning -- Bri Crabtree 2:00pm Multiplex Madness for Passing -- Poetic Motion Machine 3:00pm Fun/Simple Club Passing Patterns for 3/4/5 -- Louis Kruk 3:00pm 2 Diabolo Fundamentals and Combos -- Ted Joblin 3:00pm Kendama -- Sean Haddow (BEG/INT) 4:00pm Beginning Contact Juggling -- Kyle Johnson 4:00pm Diabolo Fundamentals -- Chris Garcia (BEG-ADV) Wednesday, July 28 9:00am IJA College Credit Meeting -- Don Lewis 9:00am YEP 1: Basic Techniques of Teaching Juggling -- Kim Laird 10:00am 3 Ball Esoterica -- Jackie Erickson (BEG/INT) 10:00am 5 Ball Tricks -- Doug Sayers & Josh Horton (INT/ADV) 10:00am YEP 2: How To Develop a Youth Program -- Kim Laird 11:00am Claymotion -- Jackie Erickson 11:00am Scaffolding:
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• Social Integration at a Public Park Basketball Court
UNIVERSITY OF CALIFORNIA Los Angeles Who’s Got Next? Social Integration at a Public Park Basketball Court A dissertation submitted in partial satisfaction of the requirements of the degree of Doctor of Philosophy in Sociology by Michael Francis DeLand 2014 ABSTRACT OF THE DISSERTATION Who’s Got Next? Social Integration at a Public Park Basketball Court by Michael Francis DeLand Doctor of Philosophy in Sociology University of California, Los Angeles, 2014 Professor Jack Katz, Chair This dissertation examines the ongoing formation of a public park as a particular type of public place. Based on four years of in-depth participant observation and historical and archival research I show how a pickup basketball scene has come to thrive at Ocean View Park (OVP) in Santa Monica California. I treat pickup basketball as a case of public place integration which pulls men out of diverse biographical trajectories into regular, intense, and emotional interactions with one another. Many of the men who regularly play at Ocean View Park hold the park in common, if very little else in their lives. Empirical chapters examine the contingencies of the park’s historical formation and the basketball scene’s contemporary continuation. Through comparative historical research I show how Ocean View Park was created as a “hidden gem” within its local urban ecology. Then I show that the intimate character of the park affords a loose network of men the opportunity to sustain regular and informal basketball games. Without the structure of formal organization men arrive at OVP explicitly to build and populate a vibrant gaming context with a diverse array of ii others.
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• Blasting at the Big Ugly: a Novel Andrew Donal Payton Iowa State University