Egg-Shaped Curves
8 hours ago
- #mathematical modeling
- #egg-shaped curve
- #geometry
- The article discusses the derivation of an equation for an egg-shaped curve that closely resembles the shape of a chicken egg, distinguishing it from other oval curves like Cassini oval.
- Basic derivation of the egg-shaped curve equation is presented, including displacement and introduction of constant values for simplification.
- The article provides equations for the major and minor axes, circumference, and plane area of the egg-shaped curve.
- Calculations for the volume and surface area of a three-dimensional egg-shaped figure are detailed, with special cases like the sphere (when b=0) highlighted.
- The use of an intermediate variable for expressing egg-shaped curves is introduced.
- Alternative methods using ellipsoids instead of circles as basic figures are explored.
- Cases where constants 'a' and/or 'b' are outside defined regions are discussed.
- General extension from egg-shaped curves to pear-shaped curves is presented, with conditions for closed curves and new constraints explained.
- Higher-order equations (8th order) are introduced, with solutions and examples provided, including interesting figures like 'spade shaped curves'.
- The article concludes with references to sites and papers citing this work.