International Research Journal of Engineering and Technology (IRJET)
e-ISSN: 2395-0056
Volume: 04 Issue: 07 | July -2017
p-ISSN: 2395-0072
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Pythagoras n-sided polygon with Natural Numbers using Programming Language S.N.R.G. Bharat Iragavarapu 1, Kuppili Sai Rahul 2 1Assistant
Professor, Department of Mathematics GVP College of Engineering (Autonomous), Visakhapatnam, AP, India 2 B.Tech Student, Department of Electronics and Communication Engineering GVP College of Engineering (Autonomous), Visakhapatnam, AP, India ---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - In this paper, using computer programming
language Java we determine the Pythagoras n-sided polygon for any (n-1) natural numbers and this Pythagoras n-sided polygon satisfies the extension of the Pythagoras theorem i.e the sum of the squares of the first (n-1) side lengths is equal to the sum of the square of the nth side length. Key Words: Pythagoras theorem, Triangle, Quadrilateral, Polygon, Pythagoras n-sided polygon
1. INTRODUCTION
Step 10: Using another for loop, calculate sum of squares of all the entered numbers. Step 11: Calculate first element of second array arr2[0] as {(2*arr1[0]*arr1[0])-sum} . Step 12: If arr2[0] is positive go to step 13, else, go to step 13. Step 13: Multiply arr2[0] with -1 and go to step 14. Step 14: Calculate the remaining elements of arr2[i] as
In [1, 2, 3, 4, 5, 6 ] the authors developed extension of Pythagoras theorem for 4, 5, 6, 7, 8, 9 sided polygons using programming language C. But, for a polygon with sides more than10 this process is difficult using programming language C.
(2*arr1[i]*arr1[0]) except the last element. Step 15: Assign the value sum for arr2[n-1]. Step 16: Use another for loop to print the elements of arr2[]. Step 17: Print the statement “Entered number of sides can’t form a polygon.”
In this paper we developed a program using programming language Java for formation of an n-sided polygon when (n-1) natural numbers are provided. This nsided polygon satisfies the Pythagoras theorem.
Step 18: Stop.
2. MAIN RESULT
Step 1: Enter number of sides of your polygon.
2.1 Algorithm
Step 2: Enter any (n-1) natural numbers.
2.2 Result Analysis
Step 3: It displays the side lengths of an n-sided polygon.
Step 1: Start. Step 2: Enter the number of sides of the desired polygon. Step 3: Read the value n defining it as k which is of integer data type.
The above procedure can be explained below : For example,
Consider a 5-sided polygon(pentagon).
Step 5: Define integer data type variables, i, j, t, sum.
Let the four natural numbers be 1, 7, 5, 8.
Step 6: Initialize t as (n+1) and sum as zero.
The side lengths of the polygon are 137, 14, 10, 16, 139.
Step 4: If k is greater than 2, go to step5, else, go to step15.
Step 7: Define arrays arr1[] and arr2[] with size n and t respectively.
The side lengths mentioned above satisfies Pythagoras theorem.
Step 8: Enter any n natural numbers. Step 9: Read those values using a for loop.
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