Scientific Calculator With The Aid Of Geometry And Based Upon It, A Mechanical Calculator

TL;DR

This paper introduces a battery-free mechanical calculator that uses geometric properties of similar triangles to perform scientific calculations like roots, logarithms, and exponents through a novel geometric method.

Contribution

It presents a new geometric approach for scientific calculations and a mechanical analogue device based on similar triangles, eliminating the need for electronic calculators.

Findings

Successfully performs scientific calculations using geometric methods

Design of a mechanical calculator based on similar triangles

Provides error-free calculations without batteries

Abstract

Scientific calculations involving multiplication, division, exponents, inverse exponents of real numbers, geometric mean, reciprocal, Euler number, logarithm, and antilogarithm are generally carried out using battery operated electronic calculators. In this paper, geometric methods employing properties of similar right angled triangles have been devised for performing error free scientific calculations without the use of batteries. Based on this method, a mechanical analogue calculator has also been designed. A right-angled triangle with one perpendicular side of unit length is drawn, and from the vertex of the right angle, a perpendicular is drawn onto the hypotenuse. From the point of intersection of this perpendicular with the hypotenuse, another perpendicular is drawn to the base, and this process is continued until n perpendiculars are drawn. The resultant figure is a right angled triangle containing n similar triangles. Using properties of similar triangles, it is found that the lengths of the first, second, third so on till last perpendicular form a geometric series. If the length of the nth perpendicular is equated to a given real positive quantity less than one, and the base angle is adjusted, then the length of the first perpendicular represents the nth root of the given quantity. If the given quantity is greater than one, its reciprocal is equated to the length of the nth perpendicular, and the reciprocal of the first perpendicular gives the nth root. In this manner, several scientific calculations can be performed using geometric techniques.