Show HN: I was curious about spherical helix, ended up making this visualization (visualrambling.space)

Article summary

The article explores the concept of a spherical helix, a shape that loops around a sphere, and how to move objects along this path in 3D space. The author uses parametric equations to define the x, y, and z coordinates of an object as functions of time, creating a helical pattern around a sphere. The article provides a step-by-step explanation of how to create this path, starting from simple circles and spirals. The author also shares their personal project, visualrambling.space, where they create visual articles on various topics.

Main themes

• Spherical helix
• Parametric equations
• 3D mathematics
• Mathematical visualization
• Geometry
• Interactive learning

What commenters say

• The article provides a good introduction to the subject, but could benefit from more advanced mathematical concepts, such as polar coordinates and linear algebra.
• The spherical helix path shown in the article is not a loxodrome or rhumb line, but rather a different type of spherical spiral.
• The article's use of parametric equations to create the spherical helix path is a useful tool for visualizing and understanding complex geometric shapes.
• The choice of z-function in the parametric equation affects the consistency and thickness of the helix, and different functions could be used to achieve different visual effects.
• The article's animations and visualizations are helpful for understanding the concept of a spherical helix, but may be confusing for some readers due to the fixed orientation of the cube.
• The points on the spherical helix path are not equally spaced, and scaling the z-coordinate affects the rate of change of the curve.
• The article's approach to creating the spherical helix path is more focused on visual appeal than mathematical accuracy or real-world applications.
• The use of parametric equations and trigonometric functions is a powerful tool for creating interactive and dynamic visualizations, and can be applied to a wide range of mathematical and artistic projects.