Infinite Surds

Infinite Surds Around 800 b.c.e, a young Indian scholar by the name of Baudhayana sat in his household studying manuscripts of previous mathematicians. He soon began his own research in mathematics and stumbled across a concept used in common mathematics today. This concept was added to a series of texts known as the Shulba Sastras. Today, the concept added to these books is known as square roots. Much like subtracting a number is the opposite of adding a number, the square root of a number is the opposite of squaring a number. For example, 32=9 ([pic]), likewise [pic]=3. A radical, another name for a square root, comes in different forms. For example, if you change the root of a radical to a 3 rather than a 2, it becomes a cube root. Instead of squaring a number, 32=9, you will cube the number, 33=27 or in other words, 3*3*3=27. Therefore, you will have to cube root it, [pic]. The square roots of most numbers don’t always come out even. The number 9, is an example of a perfect square, because the square root of 9 is 3, a rational number. On the other hand, the square root of 8, does not come out even, when calculated through a calculator, the answer is 2.828427125, an irrational number. The exact values of these irrational numbers cannot be expressed in decimal form, and must be left in radical form because the decimal values are rounded and not completely accurate. These irrational radical numbers are called surds. Surds can also be represented in series. In mathematics, given an infinite sequence of numbers (an ), a series is informally the result of adding all those terms together: a1 + a2 + a3 + · · ·. Therefore an example of an infinite series would be, [pic]as you can see the series increases by 1/2n each time. This can also be applied to surds as well, forming infinite surds. The expression [pic]would represent a basic infinite surd. These series are much more complex than basic series. Although this may be the case, the two are not that