# Pythagoras Essay

Abstract

Pythagoras theorem gives a relationship of the three sides of right angled triangles. It is extended to draw relationship among the interior angles of such right-angles triangles to form what is known as trigonometrical ratios. The theorem has vast application in science and mathematical phenomena. It is also used in the derivation of other theorems. This paper attempts to uniquely explain the theorem by experiment. Calculations and measurements will be done to arrive at stated proofs. I addition, theoretical values (value obtained through calculation) and practical ones are compared to establish the degree of error so allowed.

Introduction

Pythagoras theorem is mathematically expressed as So that c

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Calculated and measured values were compared to establish the degree of error so allowed.

The table below gives the results thus obtained. Triangle | Measurant | Calculated | Measured | R | 1 | Ѳ | 19.660 | 200 | 1.75% | | Φ | 69.980 | 69.50 | 0.7% | | hypotenuse | 7.43cm | 7.45cm | 0.3% | 2 | Ѳ | 53.50 | 53.10 | 0.75% | | Φ | 400 | 36.90 | 8.4% | | hypotenuse | 2.5 cm | 2.5 cm | 0.0% | 3 | Ѳ | 18.20 | 220 | 17% | | Φ | 6.60 | 700 | 0.6% | | hypotenuse | 3.2 cm | 3.2 cm | 0.0% | 4 | Ѳ | 75.40 | 680 | 10.9% | | Φ | 18.80 | 250 | 24.9% | | hypotenuse | 3.2 cm | 3.1 cm | 3.2% | 5 | Ѳ | 38.70 | 400 | 3.25% | | Φ | 51.40 | 600 | 14.3% | | hypotenuse | 4.6 cm | 4 cm | 15% |

The values of the third column were calculated as follows:

Ѳ = tan-1 ( oppositeadjacent)

Φ=sin-1 (opposite hypotenuse)

The hypotenuse was obtained by using the relation

Hypotenuse= adjacent2+opposite2

The value R in the 5th column is used to give percentage error; the percentage by which the measured and the calculated values differ.

It was obtained by getting (1- calculatedmeasured) x 100%

Precautions taken during measurements

The error of parallax was