Conical sections, hyperbola

thingiverse

In mathematics, a curve is defined as a result of intersecting a plane with a cone. Traditionally, three primary types of this curve exist: the ellipse and circle (with the circle being a unique instance of an ellipse), the parabola, and the hyperbola. The circle's distinctive qualities often earn it its own classification, elevating it to the fourth type of conic section. A recent project focuses on designing a model representing a hyperbola as a curve obtained from intersecting planes with cones. This undertaking also involves specifying parameters of the curve for further study and showcasing relevant calculations to students. Adding an extra layer of complexity to this challenge, designers are tasked with creating each part of the cone in a way that allows them to assemble together seamlessly into a complete cone. I designed this model using FreeCAD, taking advantage only of its fundamental building blocks. Image: A picture borrowed from wiki commons. Project: Exploring Conic Sections Objectives: The primary aim of this project is to introduce students to CAD through practical application of rotation, positioning, and boolean operations on primitives. It also provides an engaging tool for visualizing mathematical concepts. Target Audience: This project can be implemented in tandem with teaching conics' mathematical properties, making it suitable for educators seeking to enhance student understanding through hands-on learning experiences. Steps to Follow: 1. Begin by crafting a cone and a cube of suitable proportions. 2. Utilize rotation and positioning capabilities to arrange these primitives as needed, followed by the execution of boolean operations (such as subtraction) between them. 3. Review the results obtained after each operation. Expected Outcomes: Successful completion of this project allows learners to master the application of basic placement, rotation, and boolean operations on fundamental CAD elements. It also enables a deeper comprehension of the mathematical concept of conic sections through practical experience.