Ancient Chinese Number System (02:24)
At the heart of Chinese mathematics was a simple number system--a decimal place value system.
Chinese Written Numbers (01:13)
When writing numbers down, the Chinese could not use the place value system. They did not have a concept of zero, and therefore, the written number was very limited.
Chinese Magic Number Square (01:57)
Today, the Chinese still believe in the mystical power of numbers. The magic square is a precursor to the game of sudoku.
Mathematics in the Emperor's Court (02:53)
The calendar and movement of the planets were of great importance to first Chinese emperor, even influencing the way each day was planned.
Mathematics Essential to Chinese State (01:03)
Ancient China relied on mathematics to run the state itself. It had a strict legal code, widespread taxation, and a standard system of weight, measurement, and money.
Ancient Chinese Equations (01:44)
The ancient Chinese used equations to solve more and more complex problems. Used over 4,000 years ago in China, these equations were not used in the West until the 19th century.
Chinese Remainder Theorem (02:16)
Ancient Chinese astronomers used the remainder theorem to calculate the movement of planets.
Golden Age of Chinese Math (02:51)
By the 13th century, over 30 mathematics schools were scattered across China. The Emperor had a passion for quadratic and cubic equations.
Cubic Equations (01:47)
Cubic equations can solve complex problems involving complex mathematics. The solutions, however, are only approximate.
Mathematics of India (01:49)
Indians had discovered the mathematical benefits of the decimal place value system and were using it in the 3rd century. Many rank the Indian system of counting as one of the greatest intellectual innovations of all time.
Indian Mathematics: Invention of Zero (01:49)
Indians invent zero, in evidence in the 9th century but likely used for centuries before that.
Zero and Nothingness (01:36)
At the very heart of the Indian belief system lay concepts of nothingness and eternity. Nothingness is the ultimate goal of humanity. This may be why this culture invented zero.
Indian Mathematics and Father of Zero (02:42)
Brahmagupta is one of the most important mathematicians both of India and of its time. His concepts are taught today all over the world. One divided by zero equals infinity. Indians also invent negative numbers.
India: Quadratic Equations (01:40)
The Indian abstract approach to mathematics revealed a new solution to quadratic equations. Under Brahmagupta, a new language of mathematics came to life.
India: Trigonometry and Sine Functions (03:05)
Trigonometry acts like a dictionary translating geometry into numbers and back again. At its heart is the study of right-angle triangles. The sine function allows one to calculate distances without taking accurate measurements.
Mathematics: Concept of the Infinite (02:15)
Indian mathematicians search for the sine function of every angle. In the 15th century, Variyar develops the concept of the infinite. He produces a language to articulate and manipulate the infinite.
Indian Mathematics: Pi (02:27)
The 6th-century mathematician Aryabhata comes up with an approximate value of pi. Later, Variyar calculates the exact value of pi in the 15th century.
Non-Western Mathematics (01:12)
Indian mathematicians made crucial mathematical discoveries centuries before any Western mathematicians.
Muslim Scholars (01:42)
In the 7th century, the hew Islamic empire spread across the East. At the heart of the empire lay a vibrant, intellectual culture. Muslims studied astronomy, medicine, chemistry, zoology, and mathematics.
Islam: Intellectual Curiosity (02:30)
Intellectual curiosity was actively encouraged in the Islamic Empire. Learning was a requirement of God. The demands of Islam demanded mathematical skills. Algebra came out of this era.
Universal Language of Algebra (02:13)
Algebra provides systematic ways to analyze problems. Muslim mathematician Al-Kharazmi's great breakthrough came when he applied algebra to quadratic equations.
Cubic Equations and Omar Khayyam (02:18)
An 11th-century Persian poet and mathematician, Omar Khayyam developed algebra that contains the first complete treatment of the solution of cubic equations.
General Solution to Cubic Equations: Fibonacci (02:38)
Five hundred years after Omar Khayyam's work on cubic equations, Italians made the next leap towards a general solution. Europe's first medieval mathematician was Fibonacci, who promoted a new number system.
Fibonacci Sequence: Nature's Favorite Numbers (02:26)
Today, the Italian mathematician Fibonacci is best known for the number sequence now called the Fibonacci numbers. These numbers appear in nature in rabbit breeding, flower petals, and pineapple skins, to name a few.
Modern Europe's Mathematical Breakthrough (02:52)
In 16th-Century Bologna, Italy, the next major mathematical achievement appeared. Tartaglia found a formula to solve not one, but many types of cubic equations.
Western World's Mathematical Revolution (01:59)
The Italian mathematician Tartaglia shared his general solution for cubic equations with Cardano, who shared it with another mathematician. Tartaglia's achievements paved the way for a mathematical revolution.
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