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samalbee

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Equations, interesting facts and history

The term equation goes back to Leonardo Fibonacci (about 1180 to about 1250), who used it in Italian as equatio. The equality of two terms was expressed verbally for a long time, e.g. by the Latin word aequatur (equals).
In connection with the use of variables, a sign for equality became mandatory.

Today's equation sign "=" originates from the English mathematician Robert Recorde (1510 to 1558).

What progress it meant to formalize equations, i.e. to express them with the help of variables and the equals sign, can be seen in the difficulties that can sometimes arise when solving text problems - help me do my homework  (application problems). If one has found a correct formal equation here, an important step in solving the problem is often done.

In ancient mathematics, Arabic mathematics - domyhomework.club/accounting-homework/ , and European mathematics until the end of the 16th century, equations were given and solved exclusively in text form.

Example:

Thus, in a calculus book by ADAM RIES (1489 to 1559), which appeared in 1524, one finds the following task:

Someone hires a worker for 28 days under the condition that he pays him 5 pennies (per day) if he works, but that the worker pays him 3 pennies (per day) if he does not work.
When the 28 days are up, they settle their accounts and come to the conclusion that neither owes the other anything, but that neither has to give anything to the other, neither the master nor the worker. The task is now:

How many days did the worker work and how many days did he not? Today one would apply:
Number of working days: x
Number of non-working days: y

It follows: 5 x = 3 y and x + y = 28.

Then: 5 x = 3 (28 - x), which gives the solution x = 10.5 and y = 17.5.

Without using variables, the solution might be difficult to find, especially since it is not in the range of natural numbers.

Today, the letters a, b, c, etc. are preferred for the variables. This goes back to Rene Descartes (1596 to 1650).
In the old Egypt one used the word Haufe for the looked for size - homework help geometry , with the Greeks the letter τ (tau) - but only as abbreviation, not as variable - was often used, the old Indians used colors and Francois Vieta (1540 to 1603) used small Latin letters.

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