Math Tables - 5

The Existence And Benefits Of Maths Table

Introduction

Before the existence of calculators, and even during the period when they were quite scarce and expensive, people made use of mathematical tables. The mathematical table comprised of list of figures showing results of calculation with different arguments to help simplify and speed up computation to a very large extent. During this era, trigonometric function tables and logarithm tables were very common in science and maths textbook. Specialized tables were created for various applications like statistics, celestial navigation and astronomy.

Example

When one wants to compute sine 75 degrees, 8 minutes and 40 seconds by making use of a trigonometric function table, he might have to just round up 75 degrees, 10 minutes and afterwards look for 10 minutes on the 75 degrees page.

In the period before the use of electronic computers, interpolating table data was basically the only means of achieving top accuracy values of functions of maths needed for various applications such as surveying, astronomy and navigation. For one to understand the essence of accuracy in the afforested applications, he should take note that one minute of arc at sea level which is along the meridian or equator of the earth equals approximately to one nautical mile.

Hipparchus and Menelaus were the first tables of trigonometric functions. However, these two tables of trigonometric functions have been lost for a long period of time.

After the hipparchus and Menelaus, there was the Ptolemy which is known to be surviving. All these tables were tables of chords and not half cords, meaning sine function. An Indian mathematician named Aryabhata created the first sine table. After the creation of the sine table by Aryabhata, more attempts were made in improving the table’s accuracy. This led to the discovery of power series expansions of both the sine and cosine function. This was all thanks to Madhava of Sangamagrama. Madhava also tabulated sine table with accurate values up to 8 decimal places.

Conclusion

Tables of mathematics have been in existence since time immemorial. As time whirled by, new systems began to emerge. However, credit cannot be taken away from the mathematical table as it was the first step in ensuring accuracy values in mathematics

 

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