small-project

Small warm-up and fun projects using Python and C++.

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Table of Contents

1. Introduction
2. Setup and Requirements
3. Repository Structure
4. Circle Contours
5. Surface of Cylinders
6. References

Introduction

This repository contains mini fun and warm up projects. The current projects are:

• Circle Contours
• Surface of Cylinders

Setup and Requirements

Python

Python projects were written in Python3.x so at least python3.8 is needed. Used libraries;

• NumPy (pip install numpy)
• Matplotlib (pip install matplotlib)

C++

No projects have been written in C++ yet. They are upcoming.

Repository Structure

• ./Circle-contours/
• circle_contours.py : Plots colored contour lines for a circular function.
• ./Surface-of-Cylinder/
• surface_of_cylinders.py : Demonstrates OOP in Python by modeling circles and cylinders.

Circle Contours

File: circle_contours.py

Theory

This script creates a contour plot for the function: $z = \sqrt{x^2 + y^2}$ where (x, y) form a meshgrid ranging from -10 to +10 on both axes. Each contour line represents points at the same distance from the origin (0, 0). The result is a series of concentric circles, each colored differently.

Why Use Contour Plots ?

• They provide a 2D way to visualize 3D surfaces.
• Useful for understanding radial distances or levels in a data set.

Usage

1. Install dependencies:

   pip install numpy matplotlib

2. Run the script:

python3 circle_contours.py

3. A matplotlib window displays the filled contour plot with a colorbar. You’ll see circular bands of color radiating outward from the origin.

Surface of Cylinders

File: surface_of_cylinders.py

Theory ¹

A cylinder can be thought of as two parallel circles (top and bottom) plus a “curved surface” that, if cut and flattened, forms a rectangle.

• Top and Bottom Circles:

  • Radius: r
  • Area: $\pi r$²

• Curved (Lateral) Surface:

  • Unrolled into a rectangle with:
    • Height: h
    • Width: the perimeter (circumference) of the circle, $2 \pi r$
  • Area: Perimeter * Height = $2 \pi rh$

Putting these together, the total surface area S of a closed cylinder is

$$ \text{Surface} = \text{S} = 2(\pi r2) + 2\pi rh $$

where $2(\pi r$²) accounts for the top and bottom circles and $2\pi rh$ is the curved surface in rectangular form.

The volume of a cylinder is based on the area of the circle’s base multiplied by the height:

$$ \text{Volume} = \text{V} = \pi r^2h $$

Structure of Classes

In this mini-project, there are two classes:

1. Circle

   • Attributes:
     • radius
   • Methods:
     • get_area(): returns $\pi r$²
     • get_perimeter(): returns $2\pi r$

2. Cylinder (inherits from Circle class)

   • Attributes:
     • height
     • (inherits radius from Circle)
   • Methods:
     • get_volume(): uses circle’s area * height implies $\pi r$²h
     • get_surface(): uses the cylinder surface area formula: $2\pi r$² + $2\pi rh$

By extending Circle with Cylinder, we can reuse Circle’s methods (get_area, get_perimeter) for computing the volume and surface of a cylinder.

Usage

1. Run the script:

   python3 surface_of_cylinders.py   

2. Follow the prompts on the terminal to enter radius and height for cylinder. An example input and output prompts are:

   Enter radius: 5
   Circle with radius 5
   Area of the Circle is 78.53981633974483
   Perimeter of the circle is 31.41592653589793
   
   Enter height of cylinder: 10
   Cylinder with height 10 and radius 5
   Cylinder's volume is 785.3981633974483
   Cylinder's surface area is 502.6548245743669
   

References

1. Surface Area of Cylinder