Why we pull roots

Solutions of polynomial equations as "root" to refer to the polynomial has to do with one of the bizarre false reports of mathematical history

In German we move square roots. In English you talk about "Square Root Extraction". In Spanish one uses a word translation: "Extra La Raiz Cuadrada". Where does this phrase come from and what do equations have to do with the plant world?

Why we pull roots

That "House of wisdom" In Baghdad, the Blother season of Islam came together many Islamic scholars. Image: Zerseshk / Public Domain

The expression "Square root" and solutions of polynomial equations as "root" to refer to the polynomial has to do with one of the bizarre false reports of mathematical history. Some words and symbols (think of our today’s Arab numerals) found their entrance into the mathematical language of Europe over borrowings from Arab mathematical works. It was the birth of the algebra and also of certain misunderstandings.

At the formation of algebra, one identifies three different epochs: In Babylonians and Egypts, mathematical problems were simply linguistically formulated and there was no excellent word for the sought (or unknown variables, as we were said today). To this "Rhetorical algebra" followed "annotated" System in which special brands or letters enriched the rhetorical formulation. Finally, the sophisticated teaching of symbols and abstract transformation rules we know today.

At the beginning of this development, mathematicians from the Persian, Indian and Arab cultural area have made significant contributions. Even the expression "algebra" Is Arab origin. He was used by Muhammad Ibn Mūsā al-Khwārizmī in a mathematical compendium of the year 820.

The word algebra

Between the years 800 to 1300, the Arabs became heirs of the science and technology of the Egypt, Babylonian, Greeks and Romer. All types of scientific writings were collected in Baghdad, the center of the Arab Empire from the ninth century, and translated. The Bait Al-Hikma (House of Wisdom) in Baghdad became the Think tank of the caliphate. It was the collection area for the most significant scholars of that time.

Al-Khwārizmī also worked in the house of wisdom. Already during his lifetime his fame was legendary – he was considered Euclid and diophant of the Arab world. Born in the region between Persia and Uzbekistan, Al-Khwārizmī was a universal learner. He popularized together with other mathematicians the Indian numbers and wrote didactic exploits over algebraic procedures. Even his name, Al-Khwārizmī, transformed with time in ours "algorithm".

The most famous book by Al-Khwārizmī carried the title "Kitab al-Mukhtasar Fi Hisab Al-Jabr Wa’l-Muqabala", what "Compendium of invoices by supplementation and compensation" could be translated. The book was a kind "User Guide" for the solution of mathematical problems. The word "Al-Jabr" In the title, many as "add to". The first Latin catch of the work (1145) became "Liber Algebrae et almucabala" called, what the word "algebra" In the European vocabulary entered.

However, more than 80 years ago Solomon Gandz and Otto Neugebauer have shown that the interpretation mentioned above "algebra" is not true.1 Babylonian and Egyptians had developed the basic balancing techniques for centuries to become equations with a variable loose.

Gandz and Neugeauer were able to bring back Al-Khwārizmī’s sources to the Babylonians, Assyrians and Sumerer. "Gabru-Maharu" means in Assyrian Oppose or Be equal. The Arabs the mathematical technology but also the phonetics of the word and it was borrowed word "Al-Jabr", that with the Arabic word "Al-Muqabala" was identified. Gandz concluded that the title "Kitab al-Mukhtasar Fi Hisab Al-Jabr Wa’l-Muqabala" just as "Science of equations" could be translated. Two is Better – And so call in the title "Al-Jabr" and "Al-Muqabala" actually equations, once in Assyrian, another time in Arabic.

The lack of failure

However, before the Arabs took over the mathematical stafette, they had to deal with the spiritual Greek mathematics. The Greeks had a preference for geometric evidence, as this is quite vividly for "the eye" can be carried out.

The mathematical problems of that time were reduced to constructions with ruler and circle. You want to.B. Find the square root of 2 geometrical, draw a square with edge-length one. The diagonal of the square then has the desired long. For addition, subtraction and even multiplication and division of segment length, there are the corresponding geometric methods. That you could not write many of these geometric gross than simple breus computational Occupational accident, which the Pythagore revealed. The traces of the irrational numbers was so important for them that they have brought the gods a hectomy (one hundred slaughtered cattle). "Since then the oxen shiver, as often a new truth comes to the light", knew Ludwig Borne to earth.

But now: The Arab mathematicians (including Al-Khwārizmī in Baghdad) used two words for the unknown roughness in a problem: "times" and "Jidr". The first word was used for the square of the unknown, the second for the unknown gross itself.

The Arabs wanted the algebraic equations that the Greeks had forced geometric kind. For the Greeks "page" respectively. "Edge" a geometric construction the coarse to seek "pleura" in your language. The Islamic mathematicians translated "pleura" as "Jidr", because this word "Base" respectively. "lower part" means, however, in plants the "root" designated. When the first European mathematicians the word "Jidr" translated, transformed it into the Latin "radix" (like radical), the word for root, a momentum error.

Why we pull roots

One side of Liber Abaci (the book of computing). Image: Public Domain

Among other things, the translators of Johannes Hispaniensis in Seville, Gerhard von Cremona in Toledo, and Leonardo di Pisa (better known as Fibonacci) in Italy’s name "root" and this became the flogged word.2 Chapter 14 of Fibonaccis "Liber Abaci" (from 1202) wore z.B. This title: "De reperiendis radicibus quadratis et cubitis …" (From finding square and cubic roots).

From then the word was "root" both for the solution of quadratic equations, as well as for the solution of arbitrary algebraic equations. In the first case, the solution became one "square root", in the second simply the "root" the equation.

Not all mathematicians committed the mistake. The rough algebraicric Francois Viète in France and others more translated directly from the Greek originals and therefore used the word "Latus" (Page) For the unknown. The alternative terminology had already prevailed in Europe. Since then, that is driving "Find" the Schuler the tail on the forehead – an exciting story that was worthy goods, from Scheherazade in the thousand and second night to be paid.

Like this post? Please share to your friends:
Leave a Reply

;-) :| :x :twisted: :smile: :shock: :sad: :roll: :razz: :oops: :o :mrgreen: :lol: :idea: :grin: :evil: :cry: :cool: :arrow: :???: :?: :!: