The World through the Lens of Mathematics

Preface

Introduction

Chapter 1          Our Algebraic World    

The World in Fractions

1.            Divided Countries

2.            Reunited Countries 

3.            Country Capitals

4.            New Countries

5.            National Anthems

6.            National Flags

7.            Skyscrapers

8.            Shared Islands

9.            Feeding Animals

10.          Healthy Weight

SOLUTIONS

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Facts in Factors

1.            Oldest European Countries

2.            The Grand Bazaar

3.            The -stan Countries

4.            Stonehenge

5.            The Mayan Calendar

6.            National Parks

7.            Treasures of the Sea

8.            Voting and Drinking Ages

9.            Movies with Numeric Titles

10.          Penicillin and Bubble Gum

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Sequential History

1.            National Anthems Around the Globe

2.            Populations of the Seven Continents

3.            The Land Down Under

4.            From Clasp Lockers to Zippers

5.            Microwaves

6.            The Deepest Point

7.            Countries with Many Borders

8.            The Decline of the Olympic Games

9.            Ancient Olympic Games

10.          Modern Olympic Games

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Unions of Unions

1.            The United Kingdom

2.            The United Nations

3.            Continental Unions

4.            The BRICS Economies

5.            Enclaves

6.            Semi-enclaves 

7.            Icelandic Glaciers

8.            Iceland Tourism

9.            Human Development vs GDP

10.          The H-Day

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The Most Extreme

1.            The Smallest Country in Oceania

2.            The Longest Border

3.            The Deepest River

4.            The Largest River

5.            The Tallest Mountain

6.            The Wettest Capital

7.            Basalt Columns

8.            The Longest Tunnel

9.            The Shortest Land Border

10.          The Ring of Fire

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UNESCO Sites with Logarithms

1.            UNESCO World Heritage Sites

2.            Countries with the Most Heritage Sites

3.            UNESCO Heritage Cities

4.            Countries with the Least Heritage Sites

5.            Restricted UNESCO Heritage Sites

6.            Losing Heritage Status

7.            Disjoint UNESCO Heritage Sites

8.            Heritage City on a Coral Reef

9.            UNESCO Heritage Lakes

10.          UNESCO Archipelagos

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SOURCES

Chapter 2         Around the World With Equations  

Inventions with Linear Equations

1.            Driving on Causeway

2.            Linking to the Continent

3.            Temperature Scales

4.            Nobel Prize

5.            Easter Island

6.            Astonishing Excavations

7.            Rediscoveries of the Past

8.            Unsinkable

9.            Predictions, Predictions

10.          Credit Cards

SOLUTIONS

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Nonlinearities around the Globe

1.            The Cradle of Civilization

2.            Monarchies and Kingdoms

3.            The Largest Kingdom

4.            Countries with Similar Names

5.            Borders between Countries

6.            The Land of Eagles

7.            Lucky-Unlucky Numbers around the world

8.            Lucky-Unlucky Numbers in Countries 

9.            Speed Limits

10.          From Rejection to Fame

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Linear Systems Everywhere

1.            Halloween around the World

2.            Shopping Cart on Wheels

3.            Camel Caravans

4.            The Tallest Mountains

5.            Countries with Lakes

6.            The Largest Rivers

7.            Alphabets

8.            Notable Minarets

9.            The Honey Country

10.          Giving Flowers

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Nonlinear Systems through Time

1.            The Newest Capital

2.            The Sculpture Lake

3.            A National Flag with Stars

4.            Time Zones

5.            Smallest Continent, Largest Island

6.            Countries around the Globe

7.            The Narrowest Country

8.            The Lowest Points of the Continents

9.            Quadripoints

10.          A Guinness Book Record Holder

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SOURCES

Chapter 3           Wor(l)d Problems  

Profits at Markets

1.            The Vernissage Market

2.            An Eritrean Market

3.            A Fish Market

4.            An Indian Market

5.            The Tabriz Bazaar

6.            A Floating Market

7.            A Parfum Market

8.            A Historic Market

9.            A Train Market

10.          A Night Market

SOLUTIONS

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Work on Work

1.            Air Conditioning

2.            Reclaiming Land

3.            The Sagrada Familia

4.            A Beer Bath

5.            A Modern Medieval Castle

6.            After Hurricanes

7.            Notable Tunnels

8.            Remarkable Tunnels

9.            The Blue Lagoon

10.          Construction Projects

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Speed and Distances

1.            Sailing in the Caribbean 

2.            Explore Dominica

3.            The Middle East

4.            A Salesperson’s Problem

5.            Three Ancient Cities

6.            Sunset in Panama

7.            Camino de Santiago

8.            The Flattest Countries

9.            Cities with Most Airports

10.          Balkan Countries

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From Capital to Capital

1.            Island Countries

2.            Central European Capitals

3.            The Furthest Closest Capitals

4.            Multiple Capitals

5.            Capitals of Bordering Countries

6.            Popular Capitals

7.            The Closest Capitals

8.            Exceptionality of Capitals

9.            Capitals Named after Presidents, Kings and Tribes

10.          Multilingual Capitals

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Mathematics in Games

1.            Slinkies

2.            Hopscotch

3.            Rummikub

4.            Ball Games

5.            Darts

6.            Dice Game

7.            Card Games

8.            Colored balls

9.            Domino

10.          Tri-omino

SOLUTIONS

SOURCES

Miscellaneous Mixtures

1.            Olympic Games

2.            Olympic Medals

3.            Saltiest Lakes

4.            Acids

5.            Acids Everywhere

6.            Acids in Medicine

7.            Date Palms

8.            Mango Trees

9.            Grapes and Raisins

10.          Nuts Mixture

SOLUTIONS

SOURCES

World Religions

1.            The Big Five

2.            Hinduism

3.            Abrahamic Religions

4.            Buddhism

5.            Holy Books

6.            Twice-Holy Temples

7.            Minarets

8.            Cathedrals

9.            Christian Churches

10.          Statues of the Buddha

SOLUTIONS

SOURCES

Chapter 4       Geometry in The World

From Graphs to Scientists  

1.            The First Female Scholar

2.            The Founder of the First Academy

3.            A Famous Brotherhood

4.            The Designer of Paradoxes

5.            The Father of Geometry

6.            Inventors of Logarithms

7.            Creators of Analytic Geometry

8.            Scientists in the Names of Curves

9.            Authors of Famous Books

10.          Creators of Notations

SOLUTIONS

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SOLUTIONS

SOURCES

Notable Shapes

1.            Roundest Countries

2.            Squarest Countries

3.            Shapes of Pyramids

4.            The Pyramid of Giza

5.            Tombs inside Pyramids

6.            The Grand Canal

7.            The Corinth Canal

8.            Buildings with Polygons

9.            The Largest Pomelo

10.          The Heaviest Pomelo

SOLUTIONS

SOURCES

Geometric Fun with National Flags

1.            Colorful National Flags

2.            The Unity Flag

3.            Rectangles on National Flags

4.            Triangles on National Flags

5.            National Flags with Triangles

6.            National Flags with Trapezoids and Triangles

7.            Circles on National Flags

8.            National Flags with Circles

9.            Five-Pointed Stars on National Flags

10.          Six-Pointed Stars on National Flags 

SOLUTIONS

SOURCES

Chapter 5           The World in Puzzles                      

Savvy Puzzles

1.            Guinea Countries

2.            Equatorial Guinea

3.            The Largest Gas Station

4.            Mont-Saint-Michel

5.            Coral Reefs

6.            Three Genii

7.            The Braille System

8.            NATO

9.            The World’s Fair

10.          Yale Lads

SOLUTIONS

SOURCES

Number Puzzles

1.            Math is Twice the Fun

2.            Roots are Bliss

3.            The Tallest Statue

4.            Amazing Numbers

5.            Tug of War

6.            The Country Mirrors a River

7.            The Lone Star State

8.            The Sahara Desert

9.            Criminals on Banknotes

10.          Units of Measurement

SOLUTIONS

SOURCES

Grid Puzzle

1.            Languages Around the Globe

2.            Official Languages in Palau

3.            Official Languages in Australia

4.            Official Languages in the U.S. and Mexico

5.            Inventions and Complaints

6.            Discovery of Insulin

7.            Tectonic Plates 

8.            Metro in Turkey

9.            The Eifel Tower

10.          Countries Rich with Lakes

SOLUTIONS

SOURCES

Logic Puzzles

1.            Countries of the Past

2.            Capitals of Hawaii

3.            U.S. Statehood  

4.            The Northwest Territory

5.            An Insular Area

6.            The Tallest Towers

7.            Suspension Bridges

8.            Countries Rich with Islands

9.            Countries of the World

10.          The Oldest Border

SOLUTIONS

SOURCES

Biography

Dr. Natali Hritonenko is an award-winning Professor of Mathematics and Associate Dean at Prairie View A&M University. During her prolific career, Dr. Hritonenko has authored 7 books and over 150 papers. Her books are used as textbooks and translated to other languages. Dr. Hritonenko is continuously working on improving mathematical education. Dr. Hritonenko is the founder and director of PVAMU REU Site: Mathematical Modeling in the Sciences supported by NSF and Mellon Canter for Faculty Excellence.

Dr. Yuri Yatsenko holds a Ph.D. from Kiev National University (Ukraine) and Dr. Sci. degree from the USSR Academy of Sciences (Moscow). He was a professor at science, business and technology schools in Ukraine, Poland, Kazakhstan, Belgium, Canada, and USA. Since 2002, he has been a professor at Houston Baptist University. Dr. Yatsenko has published eight books and more than 200 papers in top-ranked scientific journals.