Question

The approach of mathematics has changed over the years.  Describe how the approach of mathematics began starting in Ancient Babylonia, and then discuss how it changed during the time of the Ancient Greeks.  Then, compare this to how mathematics is approached today.  Be specific in your description and explanation.

Answer 1

Babylonian Mathematics:

Babylonian mathematics refers to any mathematics of the peoples of Mesopotamia from the days of the early Sumerians through the Hellenistic period.The majority of Babylonian mathematical work comes from two widely separated periods:(Old Babylonian period)and(Seleucid period).It is named Babylonian mathematics due to the central role of Babylon as a place of study. Later under the Arab Empire, Mesopotamia it became study for Islamic mathematics.

The Babylonian mathematical tablet Plimpton 322.

Babylonian mathematics were written using a sexagesimal(base-60)numeral system.From this derives the modern day usage of 60 seconds in a minute, 60 minutes in an hour, and 360 (60 x 6) degrees in a circle, as well as the use of seconds and minutes of arc to denote fractions of a degree. It is was chosen because 60 can be evenly divided by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30.The digits written in the left column represented larger values, much as in the decimal system.The power of the Babylonian notational system consider that it could represent fractions as easily as whole numbers,thus multiplying two numbers that contained fractions was no different than multiplying integers,similar to our modern notation.

Greek Mathematics:

Greek mathematics refers to the mathematics written in the Greek language from the time of Thales of Miletus.
The Greeks were adopt and adapt useful elements from the societies they conquered,and they adopted elements of mathematics from both the Babylonians and the Egyptians. But they soon started to acknowledge contributions by individuals. By the Hellenistic period, the Greeks had presided over one of the most dramatic and important revolutions in mathematical period. Greek mathematics was based on geometry.They considered first to lay down guidelines for the abstract development of geometry.Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore.Thales established what has become known as Thales' Theorem,that a triangle is drawn within a circle with the long side as a diameter of the circle, then the opposite angle will always be a right angle.

To some extent,Pythagoras was perhaps the first to realize that a complete system where geometric elements corresponded with numbers. Pythagoras’ Theorem (or the Pythagorean Theorem) is one of the best known of all mathematical theorems.
The squaring (or quadrature) of the circle,the doubling (or duplicating) of the cube and the trisection of an angle. These problems were profoundly influential on future geometry and led to many fruitful discoveries.