ham sandwich theorem
play

Ham Sandwich Theorem Carola Wenk 3/8/16 1 CMPS 6640/4040 - PowerPoint PPT Presentation

Feb 09, 2024 •101 likes •297 views

CMPS 6640/4040 Computational Geometry Spring 2016 Ham Sandwich Theorem Carola Wenk 3/8/16 1 CMPS 6640/4040 Computational Geometry Ham-Sandwich Theorem Theorem: Let P and Q be two finite point sets in the plane Then there exists a line l such

  1. CMPS 6640/4040 Computational Geometry Spring 2016 Ham Sandwich Theorem Carola Wenk 3/8/16 1 CMPS 6640/4040 Computational Geometry

  2. Ham-Sandwich Theorem Theorem: Let P and Q be two finite point sets in the plane Then there exists a line l such that on each side of l there are at most | P |/2 points of P and at most | Q |/2 points of Q . 3/8/16 2 CMPS 6640/4040 Computational Geometry

  3. Ham-Sandwich Theorem Proof: Find a line l such that on each side of l there are at most | P |/2 points of P . Then rotate l counter-clockwise in such a way that there are always at most | P |/2 points of P on each side of l . 3/8/16 3 CMPS 6640/4040 Computational Geometry

  4. Rotation Left: 4 Right: 4 3/8/16 4 CMPS 6640/4040 Computational Geometry

  5. Rotation Left: 4 Right: 3 Rotate around this point now 3/8/16 5 CMPS 6640/4040 Computational Geometry

  6. Rotation Left: 4 Right: 4 3/8/16 6 CMPS 6640/4040 Computational Geometry

  7. Rotation Left: 3 Right: 4 rotate 3/8/16 7 CMPS 6640/4040 Computational Geometry

  8. Rotation Left: 3 Right: 4 rotate 3/8/16 8 CMPS 6640/4040 Computational Geometry

  9. Rotation Left: 4 Right: 3 rotate 3/8/16 9 CMPS 6640/4040 Computational Geometry

  10. Rotation Left: 3 Right: 4 rotate 3/8/16 10 CMPS 6640/4040 Computational Geometry

  11. Rotation Left: 4 Right: 3 rotate 3/8/16 11 CMPS 6640/4040 Computational Geometry

  12. Rotation Left: 2 Right: 4 Rotate around this point now 3/8/16 12 CMPS 6640/4040 Computational Geometry

  13. Rotation Left: 4 Right: 4 Rotate around this point now 3/8/16 13 CMPS 6640/4040 Computational Geometry

  14. Rotation Left: 4 rotate Right: 3 3/8/16 14 CMPS 6640/4040 Computational Geometry

  15. Rotation Left: 3 Right: 4 rotate 3/8/16 15 CMPS 6640/4040 Computational Geometry

  16. Rotation Left: 4 Right: 3 rotate 3/8/16 16 CMPS 6640/4040 Computational Geometry

  17. Rotation Left: 4 Right: 4 3/8/16 17 CMPS 6640/4040 Computational Geometry

  18. Proof Continued In general, choose the rotation point such that the number of points on each side of l does not change. k points m points rotate rotate m points k points 3/8/16 18 CMPS 6640/4040 Computational Geometry

  19. Proof Continued Throughout the rotation, there are at most |P|/2 points on each side of l . After 180  rotation, we get the line which is l but directed in the other direction. Let t be the number of blue points to the left of l at the beginning. In the end, t points are on the right side of l , so | Q |- t -1 are on the left side. Therefore, there must have been one orientation of l such that there were t most | Q |/2 points on each side of l . 3/8/16 19 CMPS 6640/4040 Computational Geometry

Recommend

Page 1 Pros and Cons of Sandwich Testing Top and Bottom Layer Tests can be done in parallel

Page 1 Pros and Cons of Sandwich Testing Top and Bottom Layer Tests can be done in parallel

Podcast Ch11-04 Title : Sandwich Testing Description : Sandwich Testing Strategy, Pros and Cons of Sandwich Testing, Modified Sandwich Testing Participants : Barry Kurtz (instructor); Brandon Winters, Sara Hyde, Cheng Vue, Dan Baehr

303 views • 3 slides
A sandwich theorem and a capacity bound for non-commutative graphs Gareth Boreland (Queens

A sandwich theorem and a capacity bound for non-commutative graphs Gareth Boreland (Queens

A sandwich theorem and a capacity bound for non-commutative graphs Gareth Boreland (Queens University Belfast) Joint work with Ivan Todorov (Queens University Belfast) and Andreas Winter (Universitat Autonoma de Barcelona). (arXiv:

304 views • 29 slides
The Sandwich Lettuce Cucumber Pepper sandwich Pronunciation: / san(d)w d , -w t

The Sandwich Lettuce Cucumber Pepper sandwich Pronunciation: / san(d)w d , -w t

The Sandwich Lettuce Cucumber Pepper sandwich Pronunciation: / san(d)w d , -w t / an item of food consisting of two pieces of bread with a fi lling between them, eaten as a light meal Oxford Online Dictionary Origins: The

579 views • 16 slides
BUCKLING OF SANDWICH BEAMS USING THE EXTENDED HIGH-ORDER SANDWICH PANEL THEORY AND COMPARISON

BUCKLING OF SANDWICH BEAMS USING THE EXTENDED HIGH-ORDER SANDWICH PANEL THEORY AND COMPARISON

18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS BUCKLING OF SANDWICH BEAMS USING THE EXTENDED HIGH-ORDER SANDWICH PANEL THEORY AND COMPARISON WITH ELASTICITY C. Phan 1* , G. Kardomateas 1 , Y. Frostig 2 1 Department of Aerospace

197 views • 6 slides
The Sandwich Generation: Challenges of Caring for Parents, Children, and Yourself Dr.

The Sandwich Generation: Challenges of Caring for Parents, Children, and Yourself Dr.

The Sandwich Generation: Challenges of Caring for Parents, Children, and Yourself Dr. Katherine L. Fiori Derner Institute March 20 th , 2012 The Sandwich Generation The term describing a generation of people who care for their

1.12k views • 33 slides
A Trace (of) Sandwich Christoph Rauch , Sergey Goncharov, Lutz Schr oder, Maciej Pir og TCS

A Trace (of) Sandwich Christoph Rauch , Sergey Goncharov, Lutz Schr oder, Maciej Pir og TCS

A Trace (of) Sandwich A Trace (of) Sandwich Christoph Rauch , Sergey Goncharov, Lutz Schr oder, Maciej Pir og TCS Seminar SS 2019 FAU Erlangen-N urnberg July 2, 2019 A Trace (of) Sandwich A prototype While language Syntax s =

700 views • 43 slides
OLDE SANDWICH TOWNE OLDE SANDWICH TOWNE COMMUNITY IMPROVEMENT PLAN (CIP) COMMUNITY IMPROVEMENT

OLDE SANDWICH TOWNE OLDE SANDWICH TOWNE COMMUNITY IMPROVEMENT PLAN (CIP) COMMUNITY IMPROVEMENT

Cover.jpg OLDE SANDWICH TOWNE OLDE SANDWICH TOWNE COMMUNITY IMPROVEMENT PLAN (CIP) COMMUNITY IMPROVEMENT PLAN (CIP) PUBLIC MEETING #2 October 15, 2008 Topics Topics Topics Project Update 1) Preliminary Financial Incentive Programs 2)

522 views • 28 slides
Continuous Production of Honeycomb Sandwich Panels All Aboard with Light and Cost-efficient

Continuous Production of Honeycomb Sandwich Panels All Aboard with Light and Cost-efficient

Continuous Production of Honeycomb Sandwich Panels All Aboard with Light and Cost-efficient Technology John Sewell, EconCore Innovation Day of CFK Valley Belgium Composites and RailWay 29 June 2016, Brussels Introduction: Sandwich

487 views • 20 slides
A fast Monte Carlo algorithm for the homogeneous set sandwich problem Vincius Gusmo Pereira

A fast Monte Carlo algorithm for the homogeneous set sandwich problem Vincius Gusmo Pereira

A fast Monte Carlo algorithm for the homogeneous set sandwich problem Vincius Gusmo Pereira de S Guilherme Dias da Fonseca Celina Miraglia Herrera de Figueiredo Universidade Federal do Rio de Janeiro Sandwich Graphs A graph G 2 ( V 2 , E

633 views • 42 slides
Quantum Mechanics As a Sandwich Theory Simone Severini University College London with Adn

Quantum Mechanics As a Sandwich Theory Simone Severini University College London with Adn

Quantum Mechanics As a Sandwich Theory Simone Severini University College London with Adn Cabello (Sevilla), Runyao Duan (UTS), Laura Mancinska (IQC/NUS), Giannicola Scarpa (CWI), Andreas Winter (ICREA) Quantum Mechanics As a Sandwich

1.39k views • 95 slides
Senior Institute Mrs. Eschman & Mrs. Jones Appliances Sandwich maker Coffee maker

Senior Institute Mrs. Eschman & Mrs. Jones Appliances Sandwich maker Coffee maker

Senior Institute Mrs. Eschman & Mrs. Jones Appliances Sandwich maker Coffee maker George foreman Microwave Waffle maker Small blender or mixer cup Microwave recipes Brownie in a mug Smores Egg sandwich

107 views • 8 slides
31. Stokes Theorem Stokes theorem is to Greens theorem, for the work done, as the

31. Stokes Theorem Stokes theorem is to Greens theorem, for the work done, as the

31. Stokes Theorem Stokes theorem is to Greens theorem, for the work done, as the divergence theorem is to Greens theorem, for the flux. Both are 3D generalisations of 2D theorems. Theorem 31.1 (Stokes Theorem) . Let C be any closed

406 views • 3 slides
Sandwich problems on orientations Zolt an Szigeti Laboratoire G-SCOP INP Grenoble, France 27

Sandwich problems on orientations Zolt an Szigeti Laboratoire G-SCOP INP Grenoble, France 27

Sandwich problems on orientations Zolt an Szigeti Laboratoire G-SCOP INP Grenoble, France 27 janvier 2011 Joint work with Olivier de Gevigney, Sulamita Klein, Viet Hang Nguyen Z. Szigeti (G-SCOP, Grenoble) Sandwich problems on

1.55k views • 119 slides
29. The divergence theorem Theorem 29.1 (Divergence Theorem; Gauss, Ostrogradsky) . Let S be a

29. The divergence theorem Theorem 29.1 (Divergence Theorem; Gauss, Ostrogradsky) . Let S be a

29. The divergence theorem Theorem 29.1 (Divergence Theorem; Gauss, Ostrogradsky) . Let S be a closed surface bounding a solid D , oriented outwards. Let F be a vector field with continuous partial derivatives. Then F d

471 views • 3 slides
Kleenes Theorem 4-0 Kleenes Theorem Theorem For every language L (over

Kleenes Theorem 4-0 Kleenes Theorem Theorem For every language L (over

Griffith University 3130CIT Theory of Computation (Based on slides by Harald Sndergaard of The University of Melbourne) Kleenes Theorem 4-0 Kleenes Theorem Theorem For every language L (over a finite

422 views • 17 slides
solution Todays program 12:00 12:15 Arrival and Sandwich 12:15 12:30 Welcome 12:30

solution Todays program 12:00 12:15 Arrival and Sandwich 12:15 12:30 Welcome 12:30

Innovative plastic sorting and reprocessing solution Todays program 12:00 12:15 Arrival and Sandwich 12:15 12:30 Welcome 12:30 12:40 Presentation of Scale Up 12:40 13:20 Presentations by Capital Region of Denmark, Veolia,

457 views • 13 slides
#prep Y assembly 01-A: Sandwich IF you are building JellyBOX with the Heated Bed upgrade, please

#prep Y assembly 01-A: Sandwich IF you are building JellyBOX with the Heated Bed upgrade, please

#prep Y assembly 01-A: Sandwich IF you are building JellyBOX with the Heated Bed upgrade, please refer to the instructions on the next page 'Heated Bed Sandwich' JellyBox Build: 09_Y-Assembly In this video, we build the 'Y assembly ' = 'bed' =

91 views • 8 slides
PCP Theorem [PCP Theorem is] the most important result in complexity theory since Cooks

PCP Theorem [PCP Theorem is] the most important result in complexity theory since Cooks

PCP Theorem [PCP Theorem is] the most important result in complexity theory since Cooks Theorem. Ingo Wegener, 2005 Computational Complexity, by Fu Yuxi PCP Theorem 1 / 119 S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof

1.53k views • 120 slides
On Theorem Proving for Program Checking Historical perspective and recent developments Maria

On Theorem Proving for Program Checking Historical perspective and recent developments Maria

Outline Introduction Where is theorem proving in program checking Inside theorem proving Big and little engines together: a new theorem proving style Decision procedures with speculative inferences Current and future challenges On Theorem

944 views • 69 slides
Intergenerational Transfers of the Sandwich Generation in Taiwan An Application of the

Intergenerational Transfers of the Sandwich Generation in Taiwan An Application of the

Intergenerational Transfers of the Sandwich Generation in Taiwan An Application of the National Transfer Accounts Method Kevin Yu-Ching Hsieh (yqxie1996@hotmail.com ) and An-Chi Tung (actung@econ.sinica.edu.tw) September, 2017 (Very

542 views • 11 slides
The Replacement Theorem Theorem (Theorem 1.10) Let V be a vector space and suppose G and L are

The Replacement Theorem Theorem (Theorem 1.10) Let V be a vector space and suppose G and L are

The Replacement Theorem Theorem (Theorem 1.10) Let V be a vector space and suppose G and L are finite subsets of V such that V = Span ( G ) , |G| = n , L is linearly independent, and |L| = m . Then m n and there is a set H G , such that

468 views • 36 slides
Linear sandwich semigroups Igor Dolinka sc:ala seminar , 10 December 2015 The bad news. . . . .

Linear sandwich semigroups Igor Dolinka sc:ala seminar , 10 December 2015 The bad news. . . . .

Linear sandwich semigroups Igor Dolinka sc:ala seminar , 10 December 2015 The bad news. . . . . . all groups will be monoids with no identity. Igor Dolinka 1 Linear sandwich semigroups The good news. . . . . . all sandwiches are vegan,

1.1k views • 95 slides
1 What is a Theorem Prover? What is a Theorem? Theorem: A formalizable statement which is

1 What is a Theorem Prover? What is a Theorem? Theorem: A formalizable statement which is

Prerequisites Course 2D1453, 2006-07 Undergraduate logic and discrete maths CS literacy Advanced Formal Methods Some functional programming experience useful The theorem prover Isabelle is programming in SML Some SML

644 views • 4 slides
22. Greens Theorem Theorem 22.1 (Greens Theorem) . If C is a positively oriented closed curve

22. Greens Theorem Theorem 22.1 (Greens Theorem) . If C is a positively oriented closed curve

22. Greens Theorem Theorem 22.1 (Greens Theorem) . If C is a positively oriented closed curve enclosing a region R then curl F d r = F d A. C R The circle in the centre of the integral sign is simply to emphasize

355 views • 4 slides

More recommend