The four color theorem is a mathematical theorem that states that, given a map, no more than four colors are required to color the regions of the map, so that no 2 regions that are touching (share a common boundary) have the same color. This theorem was proven by Kenneth Appel and Wolfgang Haken in 1976, and is unique because it was the first major theorem to be proven using a computer. This proof was first proposed in 1852 by Francis Guthrie when he was coloring the counties of England and realized he did not need more than four colors to color the map. Either he or his brother published this theorem (you only need four colors to color a map) in The Athenaeum in 1854. Many people had tried to solve this and had failed, two notables who had tried were, Alfred Kempe (1879) and Peter Guthrie Tait (1880). Many mathematicians kept failing until around the 1960s – 1970s when German mathematician Heinrich Heesch developed a way to use computers to solve proofs. And by 1976 Kenneth Appel and Wolfgang Haken, at the University of Illinois had stated that they had proven the theorem. They had used two technical concepts to prove that there was no map that had the smallest possible regions that required five colors. The two concepts were: 1. An unavoidable set contains regions such that every map must have at least one region from this collection. 2. A reducible configuration is an arrangement of countries that cannot occur in a minimal counterexample. If a map contains a reducible configuration, then the map can be reduced to a smaller map. This smaller map has the condition that if it can be colored with four colors, then the original map can also. This implies that if the original map cannot be colored with four colors the smaller map can't either and so the original map is not minimal. What they had done was use mathematical rules and procedures to prove that a minimal counterexample to the four color conjecture could not exist. They had to check around 1900...

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Pythagorean Theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:
In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two...

...The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and philosopher, Pythagoras. Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy. He is credited with many contributions to mathematics although some of them may have actually been the work of his students.
The Pythagorean Theorem is...

...Thales’ Theorem
Thales’ Theorem simply states that if three points exist within a circle, and one of those points is the diameter of the circle, then the resulting triangle will always be a right triangle. This simple idea can become very useful for certain applications such as, identifying the center of a circle with its converse. On the triangle the vertex of the right angle always terminates at the ends of the diameter line. By locating the two points of...

...In mathematics, the Pythagorean Theorem — or Pythagoras' theorem — is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:
In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
The theorem can...

...thought that perhaps, the only colour in real life is white? White light is indeed the bearer of all colours. The colours we see are reflections bouncing off an object or are the light source itself. The light sources change and the colours with them. Colour is not a stable affair. Colour is light alone, but our experience is so direct that we trust our eye and believe that a colour is inherent...

...In mathematics, the Pythagorean theorem — or Pythagoras' theorem — is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:
In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
The theorem can...

...Colours for living and learning
The Universe is a magnetic field of positive and negative charges, constantly vibrating and producing electro-magnetic waves. Each of these has a different wavelength and speed of vibration; together they form the electro-magnetic sphere. White light when seen through a prism or water vapour splits into the colours of the spectrum. Of all the electro-magnetic sphere it alone can be seen. Radio waves, infra-red waves, ultra-violet...

...Fermat's Last Theorem
Fermat's Last Theorem states that no three positive integers, for example (x,y,z), can satisfy the equation x^n+y^n=z^n if the integer value of n is greater than 2. Fermat's...