Vergleich indische und westliche Geometrie


The diagonal chord of the rectangle makes both the squares that the horizontal and vertical sides make separately.
— Sulba Sutra
(8th century B.C.
)

Vedic Math - Pythagorus


The square of the hypotenuse of a right angle triangle is equal to the sum of the squares of the other two sides.
— Pythagorean Theorem
(6th century B.C.)

Pythagorean Theorem

 

http://www.vedicsciences.net/articles/vedic-mathematics.html



Mathematics

 

 

India is often credited with contributing to the world, via Arabia, our current numerals and the concept of "zero."

Hindu mathematicians certainly formulated an ingenious system of mental arithmetic used in astronomical calculations.

This science of Vedic mathematics was revived quite recently by a prominent sannyasi, Swami Bharati Krishna Tirthaji (1884–1960).

From only sixteen Sanskrit sutras (aphorisms) he expounded a whole mathematical discipline, by which normally lengthy calculations can be performed almost instantaneously.

His writings include a concise proof of Pythagoras's theorem and a Sanskrit verse that codifies the value of pi to thirty-one decimal places. Vedic mathematics is currently taught in some British schools.

http://mathomathis.blogspot.in/2011/06/mathematical-basis-of-vedic-literature.html

Indien im 6.Jahrhundert
Indien im 6.Jahrhundert
Vedic mathematics is another example of its contribution to world progress. It is an ancient development that continues to play an important part in modern society. Without the advancements in math that had been established by Vedic culture as far back as 2500 BC and passed along to others, such as the Greeks and Romans, we would not have many of the developments and inventions that we enjoy today. The Greek alphabet, for example, was a great hindrance to calculating. The Egyptians also did not have a numerical system suitable for large calculations. For the number 986 they had to use 23 symbols. The Romans also were in want of a system of mathematical calculations. Only after they adopted the Indian system that was called “Arabic numerals” did they find what they needed.
The difference was that Vedic mathematics had developed the system of tens, hundreds, thousands, etc., and the basis of carrying the remainder of one column of numbers over to the next. This made for easy calculations of large numbers that was nearly impossible in other systems, as found with the Greeks, Romans, Egyptians and even Chinese. The Vedic system had also invented the zero, which has been called one of the greatest developments in the history of mathematics.
The numeral script from India is said to have evolved from the Brahmi numerals. This spread to Arabia through traders and merchants, and from there up into Europe and elsewhere. It became known as the Arabic numerals, yet the Arabians had called them “Indian figures” (Al-Arqan-Al-Hindu) and the system of math was known as hindisat, or the Indian art.
Vedic culture already had an established mathematical system that had been recorded in the Shulba Sutras. These are known to date back to at least the 8th century BC.
The Shulba Sutras were actually a portion of a larger text on mathematics known as the Kalpa Sutras. These and the Vedic mathematicians were recognized for their developments in arithmetic and algebra. Indians were the first to use letters of the alphabet to represent unknowns. But they were especially known for what they could do in geometry. In fact, geometrical instruments had been found in the Indus Valley dating back to 2500 BC. Furthermore, what became known as the Pythagorean theorem was already existing in the Baudhayana, the earliest of the Shulba Sutras before the 8th century BC. This was presented by Pythagoras around 540 BC after he discovered it in his travels to India. So this shows the advanced nature of the Vedic civilization.
The Vedic system of math, as explained in the sutras, also reduced the number of steps in calculations to merely a few that otherwise required many steps by conventional methods. Thus, this ancient science is still worthy of study today.

 

Die einfache Rechenmethode aus Indien

Ob und wie weit das Ganze etwas mit Veda zu tun hat, darüber sind sich die Experten nicht einig. Das ändert aber nichts daran, dass es eine große Hilfe für jeden sein kann, der mit schwierigen Rechnungen zu kämpfen hat. Damit lassen sich sogar ansonsten schwierige Aufgaben schnell im Kopf ausrechnen - ganz ohne Taschenrechner.

Um zu verstehen, wie diese ungewöhnliche Art des Rechnens funktioniert, müssen Sie etwas umdenken. Angenommen, Sie möchten 98 mit 72 multiplizieren. Vergessen Sie bitte für einen Moment, wie Sie dabei früher in der Schule (ohne Taschenrechner) vorgegangen sind. Stattdessen rechnen Sie folgendermaßen:

  • Zuerst rechnen Sie 100 minus 98, das Ergebnis ist 2, und 100 minus 72, das ergibt 28.1
  • Nun wird überkreuz gerechnet: Von den 72 ziehen Sie 2 ab = 70 und die 28 multiplizieren Sie mit 2 = 56.2
  • Anschließend werden die beiden Ergebnisse nur noch hintereinandergeschrieben und das Ergebnis ist 7056.3

Die vedische Mathematik ist aber weit mehr als nur eine bloße Rechenmethode - sie basiert zum Teil auf der Mathematik, wie sie auch in der Natur vorkommt (z.B. die Fibonacci-Spirale). Es ist zugleich eine Philosophie, die in der westlichen Welt nur wenig bekannt ist. Wer sich intensiver damit beschäftigen möchte, sollte in die vedische Philosophie hineinschnuppern.