ON THE CHINESE CHECKER SPHERE. Mine TURAN, Nihal DONDURMACI ÇİN DAMA KÜRESİ ÜZERİNE



Similar documents
Summary: Vectors. This theorem is used to find any points (or position vectors) on a given line (direction vector). Two ways RT can be applied:

32. The Tangency Problem of Apollonius.

Intro to Circle Geometry By Raymond Cheong

N V V L. R a L I. Transformer Equation Notes

Vectors Summary. Projection vector AC = ( Shortest distance from B to line A C D [OR = where m1. and m

XML Data Integration using Fragment Join

Chapter. Contents: A Constructing decimal numbers

Random Variables and Distribution Functions

Orbits and Kepler s Laws

Words Symbols Diagram. abcde. a + b + c + d + e

CLOSE RANGE PHOTOGRAMMETRY WITH CCD CAMERAS AND MATCHING METHODS - APPLIED TO THE FRACTURE SURFACE OF AN IRON BOLT

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review

(Ch. 22.5) 2. What is the magnitude (in pc) of a point charge whose electric field 50 cm away has a magnitude of 2V/m?

EQUATIONS OF LINES AND PLANES

Skills Needed for Success in Calculus 1

r (1+cos(θ)) sin(θ) C θ 2 r cos θ 2

Chapter 19: Electric Charges, Forces, and Fields ( ) ( 6 )( 6

Quick Guide to Lisp Implementation

(1) continuity equation: 0. momentum equation: u v g (2) u x. 1 a

Curvature. (Com S 477/577 Notes) Yan-Bin Jia. Oct 8, 2015

Analytical Proof of Newton's Force Laws

CHAPTER 31 CAPACITOR

MATH PLACEMENT REVIEW GUIDE

Continuous Compounding and Annualization

c b N/m 2 (0.120 m m 3 ), = J. W total = W a b + W b c 2.00

Screentrade Car Insurance Policy Summary

Adaptive Control of a Production and Maintenance System with Unknown Deterioration and Obsolescence Rates

Math 314, Homework Assignment Prove that two nonvertical lines are perpendicular if and only if the product of their slopes is 1.

Combinatorial Testing for Tree-Structured Test Models with Constraints

Or more simply put, when adding or subtracting quantities, their uncertainties add.

16. Mean Square Estimation

2. TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES

Chapter 23 Electrical Potential

Maximum area of polygon

Symmetric polynomials and partitions Eugene Mukhin

Mechanics 1: Work, Power and Kinetic Energy

Mechanics 1: Motion in a Central Force Field

Coordinate Systems L. M. Kalnins, March 2009

The art of Paperarchitecture (PA). MANUAL

Angles 2.1. Exercise Find the size of the lettered angles. Give reasons for your answers. a) b) c) Example

G.GMD.1 STUDENT NOTES WS #5 1 REGULAR POLYGONS

Answer, Key Homework 10 David McIntyre 1

Vectors. The magnitude of a vector is its length, which can be determined by Pythagoras Theorem. The magnitude of a is written as a.

Released Assessment Questions, 2015 QUESTIONS

Lesson 2.1 Inductive Reasoning

SECTION 7-2 Law of Cosines

Practice Test 2. a. 12 kn b. 17 kn c. 13 kn d. 5.0 kn e. 49 kn

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:

Module 5. Three-phase AC Circuits. Version 2 EE IIT, Kharagpur

50 MATHCOUNTS LECTURES (10) RATIOS, RATES, AND PROPORTIONS

Volumes by Cylindrical Shells: the Shell Method

Definitions. Optimization of online direct marketing efforts. Test 1: Two campaigns. Raw Results. Xavier Drèze André Bonfrer. Lucid.

Pure C4. Revision Notes

Figure 2. So it is very likely that the Babylonians attributed 60 units to each side of the hexagon. Its resulting perimeter would then be 360!

FI3300 Corporate Finance

Formulas and Units. Transmission technical calculations Main Formulas. Size designations and units according to the SI-units.

The remaining two sides of the right triangle are called the legs of the right triangle.

Chapter 3 Savings, Present Value and Ricardian Equivalence

How many times have you seen something like this?

Dynamic Modeling of a Generalized Stewart Platform by Bond Graph Method Utilizing a Novel Spatial Visualization Technique

End of term: TEST A. Year 4. Name Class Date. Complete the missing numbers in the sequences below.

UNIT CIRCLE TRIGONOMETRY

CS 316: Gates and Logic

10. Collisions. Before During After

AMB111F Financial Maths Notes

Multiple choice questions [60 points]

YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH

The Binomial Distribution

CS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001

Chapter. Fractions. Contents: A Representing fractions

. At first sight a! b seems an unwieldy formula but use of the following mnemonic will possibly help. a 1 a 2 a 3 a 1 a 2

NURBS Drawing Week 5, Lecture 10

Ilona V. Tregub, ScD., Professor

2 DIODE CLIPPING and CLAMPING CIRCUITS

Modelling the Role of Cloud Density on the Removal of Gaseous Pollutants and Particulate Matters from the Atmosphere

GRAVITATION 1. BASIC FORCES IN NATURE

12. Rolling, Torque, and Angular Momentum

6.5 - Areas of Surfaces of Revolution and the Theorems of Pappus

UNCORRECTED SAMPLE PAGES

Unit 6: Exponents and Radicals

Ratio and Proportion

The LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.

Review. Scan Conversion. Rasterizing Polygons. Rasterizing Polygons. Triangularization. Convex Shapes. Utah School of Computing Spring 2013

(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of

Visualization of characteristics of the contact network between spheres in 3D assembly

AREA OF A SURFACE OF REVOLUTION

MA Lesson 16 Notes Summer 2016 Properties of Logarithms. Remember: A logarithm is an exponent! It behaves like an exponent!

PHY 140A: Solid State Physics. Solution to Homework #2

Vectors Recap of vectors

Angles and Triangles

Generalized Difference Sequence Space On Seminormed Space By Orlicz Function

1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2

Lesson 7 Gauss s Law and Electric Fields

INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS

4.1 - Trigonometric Functions of Acute Angles

Transcription:

DÜ Fen Bilimlei Enstitüsü Degisi Sı 9 Ağustos 9 On The Chinese Cheke Sphee M. Tun N. Donumı ON THE CHINESE CHECKER SHERE Mine TURAN Nihl DONDURMACI Deptment of Mthemtis Fult of Ats n Sienes Dumlupin Univesit Küth minetun@umlupin.eu.t Geliş Tihi: 6.4.9 Kul Tihi:..9 ABSTRACT The ojet of the pesent ppe is to stu efine the sphee in ptiul meti on n etemine the piees of the sphee whih is fome these plnes. It is use the istne etween n two points t thee imensionl Chinese Cheke spe. AMS Sujet Clssifition: 5K5 5K99 Kewos: Chinese Cheke plne Chinese Cheke spe Chinese Cheke istne. ÇİN DAMA KÜRESİ ÜZERİNE ÖZET Bu çlışm öel metikli uın küei tnımlk küei oluştun pçl elilenmektei. Bunu pken öel metik olk üç outlu Çin Dm Uın iki nokt sınki uklığı veen Çin Dm metiği kullnılmktı. Anht Kelimele: Çin Dm ülemi Çin Dm uı Çin Dm uklığı.. INTRODUCTION In Chinese Chekes gme the stle of movement is fom southwest to nothest fom est to west n noth n south. Kuse E. F. [5] keeping this ule in min ske the uestions of how to evelop meti whih woul e simil to the movements me pling Chinese Chekes. Chen G. [] hs intoue the meti C L S whee L m n min S Y in the nltil plne. The Chinese Cheke plne 7. The ove meti n e genelie n the Chinese Cheke spe of imension thee n e intoue using this meti in thee imensionl nlitil spe fo n two points X n geomet hs een stuie n impove up to now see 4 6 whee C L S m L n

DÜ Fen Bilimlei Enstitüsü Degisi On The Chinese Cheke Sphee Sı 9 Ağustos 9 M. Tun N. Donumı min S inste of the well known Eulien meti E whee n. 4 In this wok the Chinese Cheke sphee t the Chinese Cheke spe hs een intoue n genel sphee eution hs een fomulte. Thought this stu we wite CC inste of Chinese Cheke fot he ske of shot.. CHINESE CHECKER METRIC FOR THREE DIMENSIONAL SACE In [4] In thee imensinol CC spe points lines n plnes e the sme with in Eulien se. It n e shown tht if : C S L C. whee C is meti spe.. CHINESE CHECKER SHERE In this wok we now efine CC-sphee poeeing oing to use nologous Eulien pesiption. : X M X C C tht is : X M X M X C S L min m. n M. Theoem.: The set C given Eution. is CC-sphee. oof: Consie. one n see tht the eutions with solute vlue epessions must e solve in ll the possile ses of. We give the pof fo one se fo the othe ses the pof simill. A B C D E F G H I J K L M

DÜ Fen Bilimlei Enstitüsü Degisi On The Chinese Cheke Sphee Sı 9 Ağustos 9 M. Tun N. Donumı Let. We otine fo the suses whee. hs solution If then in the omin we tke emin of the line in the omin we tke emin of the line in the omin we tke emin of the line If then in the omin

DÜ Fen Bilimlei Enstitüsü Degisi On The Chinese Cheke Sphee Sı 9 Ağustos 9 M. Tun N. Donumı 4 we tke emin of the line in the omin we tke emin of the line in the omin we tke emin of the line If then in the omin we tke emin of the line in the omin we tke emin of the line

DÜ Fen Bilimlei Enstitüsü Degisi Sı 9 Ağustos 9 On The Chinese Cheke Sphee M. Tun N. Donumı in the omin we tke emin of the line 4 If then -+-+-= ==-+-= ==++-= ==+-+= then -<- in the omin =-++-= = = we tke emin of the line ++ in the omin =-+-+= = için = için we tke emin of the line -<- in the omin =+-+-= = = we tke emin of the line 5If then -+-+-= ==--+= ==-+-= 5

DÜ Fen Bilimlei Enstitüsü Degisi Sı 9 Ağustos 9 On The Chinese Cheke Sphee M. Tun N. Donumı ==+-+= -<- in the omin =--+-= = = we tke emin of the line +<+ in the omin = -+-+= = = we tke emin of the line +<+ in the omin =+-+-= = = we tke emin of the line 6 If then -+-+-= ==---= ==-+-= ==+--= +<+ in the omin = --+-= = = we tke emin of the line +<+ in the omin 6

DÜ Fen Bilimlei Enstitüsü Degisi Sı 9 Ağustos 9 On The Chinese Cheke Sphee M. Tun N. Donumı = -+--= = için = için. we tke emin of the line iken ->- in the omin =+-+-= = = we tke emin of the line 7 If then -+-+-= ==--+= ==-+-= == +-+= ++ in the omin = --+-= = = we tke emin of the line -- in the omin = -+-+= = için we tke emin of the line = için +>+ in the omin =+-+-= = 7

DÜ Fen Bilimlei Enstitüsü Degisi Sı 9 Ağustos 9 On The Chinese Cheke Sphee M. Tun N. Donumı = we tke emin of the line 8If then -+-+-= ==---= ==-+-= ==+--= ->- in the omin = --+-= = = we tke emin of the line ->- in the omin = -+--= = = we tke emin of the line ->- in the omin =+-+-= = = we tke emin of the line Emple. CC-sphee with ius = n entee t M = C X : M X M X L S m min In thjs emple the CC-sphee n e onstute using the theoem.. Gph of CC- sphee n e esil wn if it is epesente n eution of the fom given in theoem.. Gph of some of the CC-sphee e given figue. 8

DÜ Fen Bilimlei Enstitüsü Degisi Sı 9 Ağustos 9 On The Chinese Cheke Sphee M. Tun N. Donumı Figue. CC sphee with ius of = n entee t M = sle moel Figue. Chnge spet of the CC-sphee. sl moel Figue. CC sphee with ius of = n entee t M =. the shpe of CC- sphee one in eight 9

DÜ Fen Bilimlei Enstitüsü Degisi Sı 9 Ağustos 9 On The Chinese Cheke Sphee M. Tun N. Donumı REFERENCES [] Donumı N. On The Chinese Cheke Spe MsC Thesis Dumlupın Univesit Deptment of Mthemtis 8. [] Akç Z. K R. On The Distne Fomul in Thee Dimensionl Ti Spe Honi Jounl Vol. 7 No.5 5-5 4. [] Chen G. Lines n Ciles in Ti Geomet MsC Thesis Centl Missout Stte Univesit Deptment of Mthemtis n Compute Ciene 99. [4] Gelişgen Ö. K R. n Ön M. Distne Fomul in the Chinese Cheke Spe Int. J. ue Appl. Mth. 65-44 5. [5] Kuse E.F. Ti Geomet Aison-Wesle Menlo k Clifoni 975. [6] Tun M. On the Chinese Cheke Conis h.d. Thesis Osmngi Univesit Deptment of Mthemtis 4. [7] Um A.Ç. Chinese Cheke Cile n Its popeties MsC. Thesis Osmngi Univesit Deptment of Mthemtis. [8] http: www. jgmes.om/hinesehekest 4