# Mathematics (especially geometry and algebra) Mathematics (especially geometry and algebra)
The answer to the diagonal of a 40 by 10 rectangle is recorded on a Babylonian tablet now held in Berlin as 40 + 102/ (2 40). As a beneficial approximation rule, the formula used here (that the square root of the sum of a2 + b2 may be inferred as a + b2/2a) often appears in later Greek geometric writings. Here we see two examples of how the Babylonians used mathematics to analyze geometry through the use of roots.

They also show that about a thousand years before the Greeks employed it, the Babylonians had figured out the link between the hypotenuse and the two legs of a right triangle. (now commonly known as the Pythagorean theorem). Try not to worry too much and look at their webpage if you’re struggling with percentage (%) questions. A typical problem discovered on Babylonian tablets is determining the value of the base and height of a rectangle, given the product and sum. The scribe used this information to determine that the difference was (b h)2 = (b + h)2 4bh.

Similarly, if we knew the product and the differential, we could determine the total. Once we had the sum and difference, we could also choose the other side by solving the corresponding equations2b = (b + h) + (b h) and 2h = (b + h) (b h). Finding the solution to the general quadratic in one variable is a good analogy for this procedure. However, there are examples when the Babylonian scribes used the same quadratic formula

The scribes realized that their solution methods were generalizable. Still, they always described these methods in specific cases rather than the derivation of general equations and identities. Rrevealing a lack of algebraic symbols. This meant they couldn’t provide comprehensive justifications for their approach to the problem’s resolution. Their use of sequential methods rather than equations is less likely to detract from a judgment of their work. Today that algorithmic techniques like theirs are common because of the introduction of computers.

These same Babylonian scribes also knew that the relation b2 + h2 = d2. Holds for every rectangle with a given base (b), height (h), and diagonal (d). Choosing the first two terms at random increases the likelihood that the third term will be irrational; however, there are situations where all three terms are integers, such as (3, 4, 5). (5, 12, 13).

(Pythagorean triples)

d2/h2 values in another column show the right line order: [1 59 0] 15, [1 56 56] 58 14 50 6 15,…,  23 13 46 40. As a consequence, the diagonal-base angle shifts from a little over 45 degrees to under 60 degrees. The scribe found all number triples since 2d/h = p/q + q/p and 2b/h = p/q q/p for. all integers p and q. Academics debate the table’s design and purpose, but its knowledge is unquestionable.

Combining astronomy and mathematics

Babylonian sexagesimal computations are orders of magnitude more powerful than those needed for the source problem texts.. Forecasting the arrival of big occurrences like lunar eclipses and the beginning. End of planetary cycles was the original motivation for the study of astronomy (conjunctions, oppositions, stationary points, and first and last visibility). They devised a system for deducing these coordinates by adding the relevant terms in an arithmetic progression. After gathering the information, the scribe would make a table algebra. Outlining the impending positions for as long as they deemed necessary. (Despite being a mathematical procedure, the results can be visualised; the tabulated numbers provide a linear “zigzag” approximation to the true sinusoidal oscillation.)

Thanks to computational techniques, astronomers were able to forecast parameters like periods, angular range between highest and lowest values, etc.

Experts see many similarities. Greek mathematics’ “application of area” technique resembles various Babylonian quadratic procedures (see below) algebra although in a geometric, not arithmetic, form). Greek geometric calculations employed the Babylonian square root approach, and technical language may have been similar.

Experts see many similarities. Greek mathematics’ “application of area” technique resembles various Babylonian quadratic procedures (see below) (although in a geometric, not arithmetic, form). Greek geometric calculations employed the Babylonian square root approach, and technical language may have been similar. Although the Greeks provided a spark for the development of modern Western mathematics,. The older Mesopotamians deserve most of the credit. The algebra details of when and how this occurred are unclear owing to a lack of unambiguous documentation.

Experts see many similarities. Greek mathematics’ “application of area” technique resembles various Babylonian quadratic procedures (see below) (although in a geometric, not arithmetic, form). Greek geometric calculations employed the Babylonian square root approach, and technical language may have been similar.