The Ultimate Chess Strategy and Tactics Guide

Chess is one of the oldest and most difficult games in the world. Although anyone can learn to play it, it requires a special kind of skill to master it. It often takes years of practice and studying to be able to excel in the kind of planning ahead that a chess master must make to win a chess game.

General Fundamentals of Strategy

In any chess game, you must do three things: protect your kind, capture enemy pieces, and capture the enemy King. To do this, you need to have a general strategy whereby you are always thinking ahead. Try to stay two or three moves ahead of your opponent. As you become more familiar with the game, what people are more likely to do is become familiar with the moves others are more likely to get.

General Fundamentals of Tactics

There are also some more general tips you should follow as well. Make your first plays wisely so that the game will suit your style of play. If you’re a tactical player, don’t choose to open with the color that goes first. Going second in chess is always an advantage. Take the time to build your strategy. Don’t ever just rush in or you waste valuable pieces. To protect your King, try to control the center of the board. This way, you have pieces that can attack from anywhere.

Tactics and Strategies for Opening

When possible, try to go second in a game. Consider your first moves carefully. In the opening phase of the game, you are working to put your pieces in the best possible place on the board. You want your pieces to be able to move freely whilst still protecting the King. This means surrounding the King with Pawns without restricting the pieces that can move more freely. To accomplish this, you have to develop the Knights before the Queen’s Bishop. As you progress, remember that it’s not good to exchange a Bishop for a Knight in the earlier stages.

Tactics and Strategies for Middle Game

The middle phase starts when you start to really attack your opponent after gaining an advantage. When you get to this portion, things become a lot more fluid and you’ll start reacting to your opponent’s moves more heavily. Don’t be afraid to sacrifice pieces here if they can get you into the perfect spot to end the game. If you can exchange a Knight or a Bishop for a Pawn, you would have gained a great advantage. A great move is called the “double threat” whereby a single chess piece is used to threaten two other pieces. Another move is called “the pin” whereby one of the opponent’s important pieces is threatened while another piece is in the way.

Tactics and Strategies for End Game

The last phase is when someone takes their opponent’s King. If you’ve done things right, you should be in a position to check – and checkmate – the King with few difficulties. By this time, you should be some pieces down and have captured many of your opponent’s pieces, including the Queen, the biggest obstacle. You need to back the opponent’s King into a corner so that it cannot take the piece you are trying to check with. If you can corner the King, you win the game, and that’s the entire point of the game. When you have material advantage, it’s best to strip your opponent so that there’s only the King to contend with. Ty to keep your Castles or Queen because they are very useful when you are trying to immobilize your opponent’s King.

Please use the following sites for more strategies and tactics to improve your chess playing:

• Chess is Fun: Explains the basics of chess games.

• Chess Strategy Ebook: Ebook containing multiple chess strategies available online.

• Predator at the Chessboards: More tactical information about chess games.

• Tips Index: Index of good chess tips for people of all skill levels.

• Chess Page: Discusses chess as well as tactics.

• Chess Trainer: Discusses chess trips from various levels of difficulty.

• Chess Tactics: Lists various chess tactics.

• The Chess Drum: A list of links to tactics based on skill level.

History of Playing Cards

Playing cards are often not given the credit they deserve. They are plucked off of a shelf because they are inexpensive, fun, and can be used multiple times. In essence, they are viewed as a game for the common people. There is, however, a rich history as to how these games came into existence.

Playing cards began in China as early as 1000 AD, under the conjoined name of pai, which, in conjunction with tiles, means “plaque”. Pai games had three major categories: games of a “money-suit system”, games that eventually evolved into a domino-like form, and a wider category that included all other forms of games, from poetry and acting to drinking games. Cards themselves were likely invented after the introduction of paper currency and games quickly evolved to match the new printed material. At this point in their evolution, they resembled thin slips of paper with dots imitating the existing twenty-one dominoes. Later on, wood and ivory were used, resulting in the dominoes we know of today. Common people could not, at this point, afford to purchase the game pieces due to the cost of production. Cards, however, did not disappear altogether. They became known as money cards and were introduced to the design of having four particular suits: coins, strings of coins, myriads of strings, and tens of myriads.

The new trend spread to the Middle East and Egypt where they developed into a system of fifty-two cards with four new suits (polo sticks, cups, coins, and swords). Playing cards arrived in Italy in the late thirteenth century and quickly scattered throughout Europe gaining the gambling connotation for which they are popularly known. In the thirteenth century, several rules specifically designed against gambling with cards were instituted. French, Latin, and Germanic sets evolved, each with their own set of suits and their own and design.

Germanic cards in particular developed an imaginative pattern of four suits with no Queen in play. Italian card makers conversely preserved the existence of the Queen for a game called Tarroco, from which Tarot cards evolved. It is the French we owe for the creation of the suits' designs of Hearts, Spades, Clubs, and Diamonds.  In the fifteenth century, once the French suits had been established, card production was expedited through the abandonment of full-color cards. Red and Black were the only colors used, allowing for stencils to be made and mass production to flourish. An interesting thing to note is how neatly playing cards mirrored the history of the time; they continue to feature popular cultural figures today, but in the time of the French Revolution, the tradition of using a King, Queen, and Jack died out in accordance with the unpopularity of the court system.  The Ace, then the lowest card, also gained special importance. When the French accepted Napoleon as emperor, the court system was reinstituted in playing cards.

In the eighteenth century, when playing cards arrived in the relatively young United States, their format changed yet again with the introduction of the Joker card, derived from a card known as the German Bauer or Americanized “Bower” when immigrants brought a game called Euchre with them from Europe. The numbers on the corners of cards, known as indexes, were also developed for the sake of simplicity. As time continued to pass, the cards were refined with rounded corners, double-ended figure illustrations, and nicer finishes for the paper used. In the nineteenth century in particular, artists began to revive the tradition of making cards ornamental, releasing countless designs featuring artwork, photographs, or even popular culture images.

Today, the playing card continues to be widely produced and used in games. Thanks to modern production methods, they are often cheap and easy to attain while remaining decorative. New materials like plastic have been introduced into card production. It is safe to assume that as time continues to pass, the playing card will continue to evolve and mirror the society through which it passes.

All You Need to Know About the Olympic Games

The Olympic games have been a set of competitions that have taken place for many years. The games, events, and medals have been a source of pride for many athletes and their home countries. The Olympics continue to be a worldwide phenomenon that many people enjoy.

History of the Olympic Games

The ancient Olympics began in the 8th century BC. The first games were held in Olympia, Greece, in an area that was dedicated to the god Zeus. Instead of receiving medals, winners were given a wreath of olive leaves and were considered local heroes in their hometowns. The original Olympic games only took place in Greece and were for Greek citizens. There were fewer sports for participation and most of them were outdoors. Some of the original sports were running contests and chariot racing. Each group of Olympic games took place every four years and lasted from one to five days in length. The games were abolished in the 4th century AD during the time of Roman rule because they were considered to be pagan practices. The International Olympic Committee was formed in 1894, and the modern Olympic games started again in 1896 in Athens. The games have continued to increase in number of participants and expand in total events. It is now one of the most popular events on earth; its games followed by millions of people.

• Winter Olympic Games

Winter sports have varied through the years, with some games being added and others ending. There are several sports that are specific to the winter games. The biathlon is a sport that started in 1924 and both men and women compete in this activity. It is a combination of rifle shooting and cross-country skiing, where participants ski to a point and then shoot a target. The bobsled is where a team rides in a sled downhill through an iced track. The track is angled and sloped, and winners are judged according to their time of completion. The sport of curling resembles a game of shuffleboard on ice. Teams push a heavy stone using brooms toward a target on a marked piece of ice. Cross-country skiing involves wearing large skis fitted for walking or sliding across snow. Individual athletes compete to cover distance across the snow. Downhill skiers wear smaller skis fitted for racing downhill. Medals are awarded for those with the best time. Figure skating is a well-known sport where couples or individuals participate in an ice-skating routine set to music. They are judged by their performance. Athletes who compete in freestyle skiing must ski a rugged course with moguls and jumps. Winners are decided by who completes the course in the best time. Ice hockey is a popular sport where teams compete to advance a puck into the competitor’s net. It consists of both male and female teams. The luge is where one to two people lie on their backs in a sled. They then travel downhill at a very fast speed through a banked course on ice. The Nordic combined is the joining of cross-country skiing and ski jumping. Participants begin with ski jumping, and then move to cross-country skiing. This sport currently is only done by men in the Olympics. The skeleton is a type of sledding that uses the same track as the bobsled or luge. The sled is not maneuvered manually; only by shifting body position and dragging the feet. Ski Jumping is where an athlete skis downhill to a ramp at the end, where they jump off. They then receive points for distance and style. Slalom skiing is skiing downhill and changing back and forth between sets of poles that are spaced about on the course. The number of poles ranges from 45-70, depending on the course. Snow boarding is similar to skiing, but on a snowboard that is attached to the feet on a boot mechanism. Athletes are judged on speed of distance and style. Speed skating is a type of ice skating race. The distances vary depending on track length, and the winner is judged by who is the fastest.

• Summer Olympic Games

The summer games also have varied through the years, with many popular sports continuing through time. In archery, athletes use a bow and arrow to shoot an arrow toward a target. Badminton is played in singles or doubles. Players use a racquet, to hit a shuttlecock back and forth across a net to score points. In basketball, teams of five players score points by making baskets through a hoop on the court. This popular game has teams for both men and women. Boxing is a supervised sport where two people fight in a ring with large gloves on their fists. Traditionally this has always been a sport for men, but the next summer Olympics in 2012 will offer it for women. Canoeing, or kayaking, is where one to two people in a boat race down a body of water. The winner of this sport is found by those with the best time. In cycling, participants ride bicycles down a course of a certain distance. Both men and women participate. Diving is jumping off a springboard into water for competition. There are different types of diving sports such as high diving and synchronized teams. The equestrian sports take horses through several arrangements to show trotting style and jumping ability. Fencing is two-person combat using swords and making moves of stabbing or thrusting with the weapon. In football, two teams of eleven players move a ball down a field for a goal at the opponents end. This Olympic sport has both male and female teams. Gymnastics includes many types of events showing flexibility and agility. Several examples are floor exercises, rings, the vault, the balance beam, and the trampoline, among others. Handball is where two teams of seven pass a ball down a court to get a goal in the net of the other team. This is done by bouncing or throwing the ball. Judo is a form of martial arts involving subduing the opponent or forcing them to the ground. It is performed by men and women, and is based on weight. In rowing, teams row a boat on a body of water, racing for time. They are judged by how much time to cover a certain distance. Several types of running events are contested during the Olympics. Some consist of short sprints, medium lengths, and the marathon. Swimming is for men and women. Athletes swim certain distances, which can be short or long. There is also synchronized swimming that is done in teams. Tennis is played in singles or doubles. Players hit a ball with a racquet back and forth across a net, playing to a high score. The triathlon is three events comprised of swimming, cycling, and running; all of which must be completed in a certain time. In volleyball, six players hit a ball over a high net using their arms and hands. Beach volleyball was introduced to the Olympics in 1992. Weightlifting has been an Olympic sport since 1920. It is a competition to see who lifts the heaviest weights according to their size. Wrestling is one of the oldest Olympic competitions. It involves two people of similar size; one person attempts to force their opponent to the ground using physical strength.

• Competing Countries

Many countries compete in the Olympics. The number has changed over the years, as some countries have abstained at times and then resumed participation. Currently there are 201 countries that participate. Each country has three-letter code as assigned by the International Olympic Committee. The countries and their codes are as follows:

1.   Afghanistan (AFG)
2.   Albania (ALB)
3.   Algeria (ALG)
4.   Andorra (AND)
5.   Antigua (ANT)
6.   Argentina (ARG)
7.   Armenia (ARM)
8.   Aruba (ARU)
9.   Samoa (ASA)
10.   Australia (AUS)
11.   Austria (AUT)
12.   Azerbaijan (AZE)
13.   Bahamas (BAH)
14.   Bangladesh (BAN)
15.   Barbados (BAR)
16.   Burundi (BDI)
17.   Belgium (BEL)
18.   Benin (BEN)
19.   Bermuda (BER)
20.   Bhutan (BHU)
21.   Bosnia and Herzegovina (BIH)
22.   Belize (BIZ)
23.   Belarus (BLR)
24.   Bolivia (BOL)
25.   Botswana (BOT)
26.   Brazil (BRA)
27.   Bahrain (BRN)
28.   Brunei (BRU)
29.   Bulgaria (BUL)
30.   Burkina Faso (BUR)
31.   Cambodia (CAM)
32.   Canada (CAN)
33.   Cayman Islands (CAY)
34.   Congo (CGO)
35.   Chad (CHA)
36.   Chile (CHI)
37.   China (CHN)
38.   Cote d’Ivoire (CIV)
39.   Cameroon (CMR)
40.   Democratic Republic of the Congo (COD)
41.   Cook Islands (COK)
42.   Colombia (COL)
43.   Comoros (COM)
44.   Cape Verde (CPV)
45.   Costa Rica (CRC)
46.   Croatia (CRO)
47.   Cuba (CUB)
48.   Cyprus (CYP)
49.   Czech Republic (CZE)
50.   Denmark (DEN)
51.   Djibouti (DJI)
52.   Dominica (DMA)
53.   Dominican Republic (DOM)
54.   Ecuador (ECU)
55.   Egypt (EGY)
56.   Eritrea (ERI)
57.   El Salvador (ESA)
58.   Spain (ESP)
59.   Estonia (EST)
60.   Ethiopia (ETH)
61.   Fiji (FIJ)
62.   Finland (FIN)
63.   France (FRA)
64.   Oceania (FSM)
65.   Gabon (GAB)
66.   Gambia (GAM)
67.   Great Britain (GRB)
68.   Guinea-Bissau (GBS)
69.   Georgia (GEO)
70.   Guinea-Equator (GEQ)
71.   Germany (GE)
72.   Ghana (GHA)
73.   Greece (GRE)
74.   Granada (GRN)
75.   Guatemala (GUA)
76.   Guinea (GUI)
77.   Guam (GUM)
78.   Guyana (GUY)
79.   Haiti (HAI)
80.   Hong Kong (HKG)
81.   Honduras (HON)
82.   Hungary (HUN)
83.   Indonesia (INA)
84.   India (IND)
85.   Iran (IRI)
86.   Ireland (IRL)
87.   Iraq (IRQ)
88.   Iceland (ISL)
89.   Israel (ISR)
90.   United States Virgin Islands (ISV)
91.   Italy (ITA)
92.   British Virgin Islands (IVB)
93.   Jamaica (JAM)
94.   Jordan (JOR)
95.   Japan (JPN)
96.   Kazakhstan (KAZ)
97.   Kenya (KEN)
98.   Kyrgyzstan (KGZ)
99.   Kiribati (KIR)
100.   Korea (KOR)
101.   Saudi Arabia (KSA)
102.   Kuwait (KUW)
103.   Laos (LAO)
104.   Latvia (LAT)
105.   Libya (LBA)
106.   Liberia (LBR)
107.   Saint Lucia (LCA)
108.   Lesotho (LES)
109.   Lebanon (LIB)
110.   Liechtenstein (LIE)
111.   Lithuania (LTU)
112.   Luxembourg (LUX)
113.   Madagascar (MAD)
114.   Morocco (MAR)
115.   Malaysia (MAS)
116.   Malawi (MAW)
117.   Moldova (MDA)
118.   Maldives (MDV)
119.   Mexico (MEX)
120.   Mongolia (MGL)
121.   Marshall Islands (MHL)
122.   Macedonia (MKD)
123.   Mali (MLI)
124.   Malta (MLT)
125.   Montenegro (MNE)
126.   Monaco (MON)
127.   Mozambique (MOZ)
128.   Mauritius (MRI)
129.   Mauritania (MTN)
130.   Myanmar (MYA)
131.   Namibia (NAM)
132.   Nicaragua (NCA)
133.   Netherlands (NED)
134.   Nepal (NEP)
135.   Nigeria (NGR)
136.   Niger (NIG)
137.   Norway (NOR)
138.   Nauru (NRU)
139.   New Zealand (NZL)
140.   Oman (OMA)
141.   Pakistan (PAK)
142.   Panama (PAN)
143.   Paraguay (PAR)
144.   Peru (PER)
145.   Philippines (PHI)
146.   Palestine (PLE)
147.   Palau (PLW)
148.   Papua New Guinea (PNG)
149.   Poland (POL)
150.   Portugal (POR)
151.   North Korea (PRK)
152.   Puerto Rico (PUR)
153.   Qatar (QAT)
154.   Romania (ROU)
155.   South Africa (RSA)
156.   Russia (RUS)
157.   Rwanda (RWA)
158.   Samoa (SAM)
159.   Senegal (SEN)
160.   Seychelles (SEY)
161.   Singapore (SIN)
162.   Sierra Leone (SLE)
163.   Slovenia (SLO)
164.   San Marino (SMR)
165.   Solomon Islands (SOL)
166.   Somalia (SOM)
167.   Serbia (SRB)
168.   Sri Lanka (SRI)
169.   Sao Tomè and Prìncipe (STP)
170.   Sudan (SUD)
171.   Switzerland (SUI)
172.   Suriname (SUR)
173.   Slovakia (SVK)
174.   Sweden (SWE)
175.   Swaziland (SWZ)
176.   Syria (SYR)
177.   Tanzania (TAN)
178.   Tonga (TGA)
179.   Thailand (THA)
180.   Tajikistan (TJK)
181.   Turkmenistan (TKM)
182.   Timor (TLS)
183.   Togo (TOG)
184.   Taipei (TPE)
185.   Trinidad (TRI)
186.   Tunisia (TUN)
187.   Turkey (TUR)
188.   Tuvalu (TUV)
189.   United Arab Emirates (UAE)
190.   Uganda (UGA)
191.   Ukraine (UR)
192.   Uruguay (URU)
193.   United States (USA)
194.   Uzbekistan (UZB)
195.   Vanuatu (VAN)
196.   Venezuela (VEN)
197.   Vietnam (VIE)
198.   Saint Vincent (VIN)
199.   Yemen (YEM)
200.   Zambia (ZAM)
201.   Zimbabwe (ZIM)

• Olympic Games….When and Where?

The first Olympic games took place in 776 BC in Olympia, Greece. There were few events, and only men were allowed. The games stayed in Greece until they were banned. When the modern games began, the first year was in Athens, Greece in 1896. Four years later, they were in Paris France, and have continued to change locations every four years. There have been Olympic games in the United States, England, Amsterdam, Norway, Belgium, Germany, Finland, Australia, Italy, Japan, Mexico, Canada, Russia, Korea, Spain, Switzerland, Austria, and Yugoslavia. The year 2008 was an enormous milestone for China, who hosted their first ever Olympic games and opened their country to visitors from around the world. The 2010 winter games will take place in Vancouver, British Columbia, and the 2012 summer games will be in London. In 2014, the winter games will take place in Sochi, Russia, and in 2016, the summer games will be in Rio de Janeiro. The first summer games were in 1896 in Athens, but winter games did not start until1924. Since then, both summer and winter were in the same year until 1992 when it started alternating every two years for each. The first winter games were in Lillehammer, Norway in 1994.

• Fascinating Facts about the Olympics

With such a long history, there are several fascinating facts about the Olympics that have occurred over time.
Original participants in ancient Olympics competed in the nude.
Women were not allowed to participate in ancient Olympics but did have their own competition, Heraea, which honored Hera, the female counterpart to the god Zeus.
Women were allowed to take part in the modern Olympics starting in 1900.
The country with the most medals awarded for the winter games is Norway, with 280 medals.
The country with the most medals awarded during the summer games is the United States with 2,189 medals.
The Olympic symbol of five rings stands for the five continents on earth.
The first Olympics that were televised were the summer games in Rome in 1960.
The last medal made of solid gold was awarded in 1912; since then medals have been plated gold.
The United States has hosted the Olympics more times than any other country.
The first Olympics in 1896 had only nine sports that were contested.
Ten sports have been dropped entirely from the modern Olympics since its inception, including polo, cricket, and motor boating.
The oldest person to win an Olympic medal was 72 years old at the 1920 games.
The Olympic games did not take place in 1916, 1940, and 1944 because of World Wars I and II.
The first year that included opening ceremonies was in 1908.
The Olympic athlete with the most medals ever was Larissa Latynina from the Soviet Union during the 1960s.

Math and Physics for Students

When it comes to school, math and physics are the subjects that are most often cited as the most difficult to master. It’s no surprise since the subjects deal with a huge amount of information which can be quite complicated. As a result, many students struggle with math and physics. Here are  some sites to help with that problem.

Fractions and Decimals

• Continued Fractions: An introduction to continued fractions.
• Fractions Fast Facts: Explains the basic facts about fractions.
• Continued Fractions Introduction: Provides good information about continued fractions.
• Working with Fractions: Shows students how to work with fractions.
• Multiplication of Fractions: Illustrates how to multiply fractions.
• Introduction to Decimals: Discusses decimals and their uses.
• Repeating Decimals: Shows how to deal with repeating decimal problems.
• Multiplying Decimals: Walks students through a few problems that involve multiplying decimals.
• Converting Decimals to Fractions: Teaches students how to properly convert decimals to factions.
• Operations with Decimals: An article that touches on most operations that involve using decimals.

Integers and Exponents

• Introduction to Integers: Discusses basic facts about integers.
• Interactive Integer Demonstration: An interactive feature that shows students how integers should be used.
• Unsigned and Signed Integers: Discusses the difference between unsigned and signed integers and when to use them.
• Integer Problems: Some good examples of integer problems.
• Adding Integers: Lesson plan aimed at teaching students how to add integers together.
• Manipulation of Exponents: Provides examples of problems that manipulate exponents.
• Integer Exponents: Good information on integer exponents.
• Exponent Properties: Points out the basic properties of exponents.
• Integer Exponent Problems: Walks students through the completion of integer exponent problems.
• Rules of Exponents: Discusses the basic rules that apply when using exponents.

Newton’s Laws

• Three Laws of Motion: Offers an overview of Newton’s laws of motion.
• Newton and the Laws of Motion: Explains the laws of motion with a brief description of Newton.
• Newton's First Law: Explains Newton’s First Law of Motion.
• Laws of Motion Activities: A list of links to activities that involve laws of motion for different grade levels.
• Newton and Acceleration: Shows how Newton’s laws explained acceleration.

Momentum and Inertia

• Mechanics and Momentum: Explains the mechanics of how momentum works.
• Momentum Lab: An online experiment that illustrates the theory of momentum.
• Momentum, Work and Energy: Shows how momentum is related to work and energy.
• Intermediate Momentum of Inertia: Briefly discusses inertia in the context of an experiment.
• Calculating Moments of Inertia: Clearly shows how to calculate inertia.

Electricity

• Electricity and Magnetism: Discusses electricity, magnetism, and how they are connected.
• Electricity: Provides information about electricity as well as several experiments involving electricity.
• Physics Lab: Electricity: A few electricity experiments to help students understand how it works.
• Static Electricity Page: Provides some good information on static electricity.
• Electricity and Magnetism Links: A list of links to multiple sites with essential information about electricity and magnetism.

Famous Mathematicians

Most people cringe when the subject turns to math, a subject that just seems too dry and abstract to command the attention for very long. Fortunately for the advancement of science, there are enough people truly interested in mathematics that the rest of us enjoy their discoveries, often without even being aware of them. Though they may seem eccentric at times, mathematicians are real people, too, and they don’t usually think of themselves as peculiar. In fact, they often think of themselves as artistic sorts. Sofia Kovalevskaya, one of the most famous mathematicians in history, even said it’s impossible to be a mathematician without being a poet in soul.

Zero - The number zero wasn’t known, understood, or used until the 13th century.

Money - Without math, and zeroes, we would never know how much money we have.

Gravity - Thanks to a famous mathematician, we know it’s gravity that keeps us from drifting off into space.

Sofia Vasilyevna Kovalevskaya, 1850 to 1891, Russia

Kovalevskaya’s interest in mathematics started when she was just a young girl in Moscow, where girls were not allowed admission to universities. She needed a man’s permission to study elsewhere in Europe and her father would not consent so she and a paleontology student, Vladimir Kovalevskaya, arranged a marriage so that, with her husband’s permission, she could study in Germany. She eventually earned a doctorate in mathematics summa cum laude based on her research alone, without ever taking the usual exams; she was the first female to earn a doctorate in mathematics in Europe. Stockholm University appointed her a position as Professor Ordinarius, another first for women in northern Europe, and rules were changed to allow her to hold a chair in the Russian Academy of Sciences although she was never allowed to become a professor in her home country.

During her lifetime, Kovalevskaya enjoyed friendships with Charles Darwin, Thomas Huxley, and George Eliot. Her most famous work, the Cauchy-Kovalevski theorem, is applicable to the fields of mechanics, differential equations, and analysis. Other works involved the rings of Saturn and the refraction of light. Three movies have been made and one book written about her life. To this day, the Sofia Kovalevskaja award is given every other year to up-and-coming researchers in Germany. Kovalevskaya had one daughter, named Sofia, who she called Fufa. Kovalevskaya’s husband, with whom she’d always had a troublesome relationship, committed suicide in 1883, in fear of prosecution for his part in a stock swindle. After an Italian holiday, Sofia caught the flu and died at the age of 41. There is a crater on the moon named for her.

Women's Rights - Kovalevskaya was involved with women's rights as well as mathematics.

Awards - Kovalevskaya won awards and university posts throughout Europe.

Multiplication - In spite of her uncommon mathematical ability, she claimed to be weak in the multiplication tables.

Blaise Pascal, 1623 to 1662, France

When Blaise Pascal lost his mother when he was just three, his father assumed the role of full-time tutor to young Blaise and his two sisters. The boy showed an immediate mathematical ability, even writing proofs famous mathematicians of the day would argue and debate with serious intent. His first work to bear his name, the Pascal theorem, was published when he was just 16. In time, Pascal’s work involved the study of hydrostatics and hydrodynamics, which led to his invention of the hydraulic press and the syringe and allowed him to prove scientifically how barometers work. Criticism of his work on the barometer led him to describe in writing his concept of the scientific method, a definition that is considered the foundation for all scientific experimentation today.

Pascal’s probability theory proved the risk in a game of chance, an outcome referred to as “the odds” today. This theory provides the basis for thousands of games of chance enjoyed today and it’s proven itself invaluable in the field of economics as well. Economics played a pivotal role in Pascal’s life when his family wealth dropped from 66,00 livres to about 7,300 when the Thirty Year War led to defaults on government bonds the elder Pascal has invested in. Pascal’s invention, the Pascaline, was a mechanical calculator that proved its use when his father got a job as commissioner of taxes in war-ravaged Rouen but was more expensive to make than the wages it was intended to replace. The Pascaline has evolved into today’s analog odometers and water meters.

Pascal suffered medical ailments all his life, including migraines, digestive disorders, and hypochondria that stemmed from a carriage accident when he was 31. It is thought he lived in pain most of his life and, never marrying, he relied on his sister, Jacqueline, to nurse him through the rough spots. Of marriage, he once described it as “the lowest of the conditions of life permitted to a Christian.” He feared Jacqueline’s convent was becoming too cult-like, experienced a religious conversion himself, and endured sibling squabbles over how inheritances should be invested. An autopsy performed at his death at age 39 revealed the mathematician might have suffered from a brain lesion, stomach cancer, and tuberculosis. There is a crater on the moon named for him.

Probability - Pascal’s probability theory in simple terms.

Theology - Pascal’s Pensees (“Thoughts”), published posthumously, is said to be a masterpiece of theological insight.

Vacuum - Rene Descartes describes Pascal as having “too much vacuum in his head.”

Johann Carl Friedrich Gauss, 1777 to 1855, Kingdom of Hanover (Germany)

This child prodigy grew up to be called the Prince of Mathematicians, the greatest mathematician since antiquity, earning a reputation befitting the man who called mathematics the queen of sciences. His talent is said to have been revealed indisputably at age 3 when he pointed out errors his father was making with the family finances. Young Gauss was able to correct these errors flawlessly and entirely in his head. Gauss put that keen mind to work with the invention of the Gauss lens, used in today’s cameras; the heliotrope surveyors used to plot uncharted lands around the world; a magnetometer used to measure the magnetic field of the planet; and a version of photometer which forwarded the field of photography. These and many other inventions advanced the study of astronomy, optics, number theory, geophysics, geometry, statistics, and analysis.

Gauss lost his first wife and a son in quick succession, leaving him with a lifelong battle with depression. He outlived his second wife by 16 years and fathered six children in his lifetime. Gauss‘ father, a business man of modest success, hoped his son would follow in his footsteps but Gauss chose mathematics instead. A perfectionist to the point of neurosis, Gauss discouraged his own sons from becoming mathematicians so as not to sully the family name. Gauss hated writing and avoided committing much of his work to paper, preferring instead to arrive at his conclusions simply out of the air. He wasn’t excited about teaching, either. Gauss’ daughter, Therese, cared for him until his death, choosing to marry only after her father’s death; she was 39. There is a crater on the moon named for him.

Speech - Gauss claimed to be able to do mathematical computations before he learned to talk.

Heptadecagon - Gauss’ discovery of how to draw a heptadecagon with just a ruler and compass was hailed as the first major advance in mathematics since the time of ancient Greece. He was a 21-year-old student publishing this finding in his university dissertation.

Death - The Royal Astronomical Society published a Gauss obituary.

These famous mathematicians changed the course of history simply by seeing life from a different perspective. Even though their thought processes were based in numbers and equations and may have been a bit too esoteric for general understanding in their time and ours, they lived through the everyday dramas that people everywhere face. They endured illness both mental and physical, loved and grieved with equal intensity, dealt with difficult family relationships, disappointed their parents, angered their children, questioned the integrity of their church and government, struggled through cultural and economic adversity, spent their money in unwise ways, and made many of the mistakes we’re all too familiar with ourselves. And there are parts of the moon named in their honor.

Additional Resources

Saturn - The rings of Saturn mystified astronomers since their 1610 discovery by Galileo.

Light - Light refraction from the mathematical perspective.

Odometer - The Pascaline calculator becomes today’s odometer.

Barometer - In explaining how a barometer works, the scientific method was established.

Syringe - The syringe uses air pressure and incompressible fluid to work effectively.

Moon - The US Geological Survey’s Astrogeology Research Program lists each lunar crater by name.

Board Games of the Ancient World

Human kind has always looked for a means of escape and entertainment. Games have existed throughout most of human history, some even date back to ancient times before humans were known to have literacy skills. The game Senet has even been found in ancient Egyptian tombs. Throughout history these ancient games have endured or evolved and many are still popular today. These games include Senet, The Game of Go, Royal Game of Ur, and perhaps the most well known, Mancala.

Senet

Evidence of the game has been found in both pre-dynastic and ancient Egypt. The name of the game means "game of passing." The board consists of 30 squares arranged in three rows of ten, and uses two sets of pawns. Historians aren't sure of the games exact rules, and often debate between a few theorized options.

Gaming with the Gods - Senet and Ancient Egyptian religious beliefs
An Ancient Game of Egypt -  Playing the game of Senet
In Search of the Meaning of Senet -  Attempting to uncover the meaning of the ancient game

The Game of Go

The Game of Go is a two player game that originated in Ancient China. The game board is a 19 x 19 grid and players use black and white stones. The game's object is to control more of the board that one's opponent. Stones or groups of stones can be captured by an opponent.
The Japanese Rules of Go - How the Japanese played the ancient game
Teaching Computers The Game of Go - an article about how the ancient game can be applied to modern computer programming
The Oldest Game of Strategy - Article about a Go Club at Indiana University

The Royal Game of Ur

The Royal Game of Ur is thought to be the oldest board game ever found, it predates even Senet. Two players use dice and black and white markers to play the game. It is thought to be a predecessor of backgammon.
The Royal Game of Ur - The University of Chicago's Oriental Institute page on Ur
The Royal Game of Ur - A description of the ancient board game
The Royal Game of Ur - The British Museum page on the game

Mancala

Mancala is thought to have originated in Africa. It is one ancient game that still remains popular and is played to this day. The Mancala board can be made of many materials, most often clay or wood. It is a two player game usually played with stones, beans, seeds, or shells. The object of the game is to capture more pieces than your opponent has.
Games Crafters - The history and rules of Mancala
Mancala Playing Agent - A history of the game and an interactive example of how it's played
Mancala - Details of the game with an interactive version you can play

Games and Toys from Colonial New England

Children in Colonial New England lived a different life than children do today. Much of a child's life was taken up with Bible study and chores. Still, Colonial children found time to play. Store-bought toys were not available, so Colonial children made their own. Children played games that their grandparents had played and passed down through the generations. Many games played in Colonial times are still being played today. Rhymes, tongue twisters, riddles, singing, and story telling were also much-loved pastimes.

Popular Games and Toys

Hide and seek, marbles, tag, blind man's bluff, jump rope, hopscotch, leap frog, swinging, rocking horse and kite flying were among the many games and activities that Colonial children engaged in. Yo-yos made of wood and string and jack straws, or pickup sticks, are examples of games that children played using pieces that they made themselves.

• Games: Popular children's games of the 18^th century along with how-to instructions for making a whirligig.
• Games and Toys: Description of common games and toys played by children during Colonial times.
• Colonial Children's Games: Description of popular games and toys of the time with illustrations.
• Colonial Games: Slide show presentation of various Colonial games.
• Colonial Games, Toys, and Recreation: Facts and pictures.
• Recreation: Overview of games, toys, and other activities of Colonial children.
• Colonial Kids and Cards: Colonial card games were very different from card games played today.
• Colonial Children's Songs: Songs typically sung by Colonial children.
• Early American Music: Where songs originated and how they were changed in Colonial America.
• Colonial Games: List of popular Colonial games and how to play each.
• Battledores: Photo of rackets used in Battledores, a game similar to badminton.
• Pioneer Children: Toys and games list.
• The Revere Children: Games that may have been played by the children of Paul Revere.
• 18^th and 19^th Century Games: Common games played by children in Colonial times. Game rules, supplies, and graphics included.
• Hunt the Slipper: Game based on the Cinderella story.

Where Did Colonial Children Get Toys?

Toys were handmade from household supplies or the natural resources that surrounded the children. Wood, corn husks, apples, string, and rags were all used. If paper was available, fans and homemade drawing books could be made.

• Authentic Rag Doll: Photo of rag doll from 1765.
• Game of Graces: Photo of girl playing a Game of Graces.
• Toys and Childhood in the Early 19^th Century: Account of how the idea of toys for children developed.
• Pre-Industrial Toys: Children's toys before the industrial revolution.

Who Did Colonial Children Play With?

Parents worked long hours during Colonial times and children were often left to take care of themselves. A child's playmates usually were siblings, since families tended to be large. Children from nearby homes might also become playmates.

• 1727 Colonial America: Information about family size and dynamics.
• American Life: A comparison of Colonial life with life today.

Colonial Board Games

Board games were played on a board drawn on paper or even drawn in dirt. Nine Men's Morrice and The Game of Fox and Geese were favorite board games of the time. Beans, rocks, corn kernels or any other available item could be used as playing pieces.

• Nine Man Morris: Game rules with a printable game board. Spelling of the game's name varies.
• Game of Fox and Geese: Object of the game, materials needed and a printable game board.

Nursery Rhymes/Riddles/Tongue Twisters

Children today enjoy rhymes, riddles, and tongue twisters just as much as Colonial children did. Many familiar nursery rhymes, such as Jack be Nimble, Jack be Quick, are the same rhymes spoken by Colonial children.

• Lucy Locket Nursery Rhyme: Popular nursery rhyme with illustration.
• Hush a By Baby: Believed to have been written in the 1600s, this rhyme was set to music and is still sung by parents today.
• Mother Goose: A scholarly exploration of Mother Goose and her association with nursery rhymes in the 18^th century.

Famous Unsolved Mathematical Problems

Pi in the sky problems that no one can solve leads one to believe that perhaps there is nothing new under the sun. Perhaps just stirring the pot of the imagination will lead to discovering the solutions to seven of the toughest mathematical problems that no mathematician, no computer, has yet to solve. The Clay Mathematics Institute has offered a million dollars for each solution.

Birch and Swinnerton-Dyer Conjecture (Number Theory)

Shorthand version of problem: Prove that an ellipse, which is a curve, possesses infinite solutions in relation to the L-series (functions, part of the analytic number theory) with a value=0 (fixed point).

Hodge Conjecture (Algebraic Geometry-Topology)

Shorthand version of problem: If X is a projective complex manifold, which cohomology (algebraic invariant) classes emanate from complex subvarieties Z?

Navier-Stokes Equations (Fluid Mechanics)

Shorthand version of problem: Prove equations describing the flow (motion/velocity) of incompressible fluids in three dimensions always are in existence and do not contain any smoothness.

P vs. NP (Computer Science)

Shorthand version of problem: Complexity Theory; are all NP (non-deterministic polynomial time) problems P (polynomial time) problems?

Poincaré Conjecture (Topology: solved in 2006)

Grigori Perelman proved the three-dimensional conjecture, the only one of the seven "Millenium" listed that has been solved. The conjecture, now a theorem, involved three dimensions, three manifolds, and a sphere.

Riemann Hypothesis (Prime Numbers)

Shorthand version of problem: Non-trivial zeros, real parts equal a half. Proven to 10 million zeros on the line by computer, but not fully solved.

Yang-Mills Theory (Quantum Physics)

Shorthand version of problem: Prove that the smallest known particle is positive. This is known as the mass gap or the difference in energy from energy in a vacuum to the next level of energy.

Equations such as the above Millennium problems are important because they describe the world and have the potential to change it. Some contend that most equations are set up and not solved, noting it is the path to solving the equations which is the most important element, not the solution, which brings the creativity and change from a math problem.

Will solving the "unsolvable" math problems create new vision for the future of humankind? Is there anything new under the sun or is it all just recycling old ideas? New ideas build off of the old foundational ideas of math that govern the world. Standing on the shoulders of mathematicians past, today's mathematicians will determine how the tiniest particle behaviors, the infinite and the finite, equations depicting the flow of energy at levels unseen, for instance, will be solved. At least the road getting there will be paved with discovery and rediscovery that will affect the world's future science and economies, perhaps changing the way humans live forever.

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Mathematical Board Games for Kids!

Math games are effective tools that provide help to many students who are struggling with the subject. In fact, a fun collection of games can improve a student's skills as well as spark an enduring interest in math. As opposed to rote memorization, a lively interactive game makes the process of learning math both entertaining and memorable. Some math games capture a student's attention by creating a familiar setting. For instance, a math game may involve putting coins in a piggy bank, shopping in a store, or saving money for a best friend's birthday gift. These games and others featuring relatable scenarios are very effective when it comes to teaching children the value and importance of math.

• Today's students enjoy a plentiful variety of games that serve to sharpen the skills found in all levels of mathematics. Interactive math games that help a student learn more about money are particularly popular with young students. A student has at his or her fingertips an entertaining selection of online games that involve learning how to count, identify, and keep track of money.

• Math games that challenge a student to learn and remember basic math facts are especially useful to younger students. Interactive games that feature themes and characters of interest to a child are effective in capturing a student's attention. A math game must stir a student's interest with its engaging themes before it begins its quest to teach a math skill.

• A game that concentrates on one skill is extremely helpful for a student with a particular challenge in a single area of math. For instance, if a student were having trouble with his or her subtraction skills, a game that focuses in on developing that skill would seem a logical choice. Many online games provide a student the opportunity to perfect a specific math skill. Addition, subtraction, multiplication, and division are just a few of the areas that a math game may focus on. There are online math games available to both younger students and students entering high school.

• A math game is a learning technique that can be of tremendous help to a student who is facing challenges in math. Furthermore, a student who begins to experience success in math class with the assistance of math games is more likely to maintain an interest in the subject throughout his or her academic career. Math skill games can turn a discouraged student into one with a renewed interest in the subject.

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