The Flat Earther's Drop to the Horizon: Explained

🌍The saying in the flat earther community that the Earth's drop to the horizon would be eight inches per mile squared is based on a misunderstanding.

📐The correct equation for the drop to the horizon on a globe is one minus the cosine of the distance to the horizon divided by the radius of the Earth, all multiplied by the radius of the Earth.

📈Using polynomial approximations, such as Chebyshev spacing, can provide a better fit for complex functions than equally spaced points.

🖊️Overleaf is a powerful tool for scientific paper writing and collaboration, allowing researchers to easily work on LaTeX documents together.

🤝Collaboration and sharing ideas in the scientific community can lead to innovative solutions and discoveries.

What is the correct equation for the drop to the horizon on a globe?

—The correct equation is one minus the cosine of the distance to the horizon divided by the radius of the Earth, all multiplied by the radius of the Earth.

Why do flat earthers believe in the eight inches per mile squared concept?

—Flat earthers believe in this concept due to a misunderstanding and misinterpretation of the drop to the horizon on a globe.

What are polynomial approximations?

—Polynomial approximations are mathematical functions that use polynomials to provide an approximate representation of a more complex function.

What is Chebyshev spacing?

—Chebyshev spacing is a distribution of points on a curve that provides a better fit for polynomial approximations compared to equally spaced points.

Can you recommend a tool for scientific paper writing and collaboration?

—Yes, Overleaf is a great tool for scientific paper writing and collaboration, allowing researchers to easily work on LaTeX documents together.

00:00Introduction: This video explores the concept of the Earth's drop to the horizon and the misconceptions in the flat earther community.

03:00Explaining the actual equation: The correct equation for the drop to the horizon on a globe involves trigonometry and the radius of the Earth.

06:45Introduction to polynomial approximations: Polynomial approximations, such as Chebyshev spacing, can provide a better fit for complex functions.

09:24The benefits of using polynomial approximations: Polynomials are easy to work with and can be used to approximate functions with a high degree of accuracy.

13:25Using RungeBot to approximate functions: RungeBot is a tool that can approximate functions using polynomial smoothing, providing a better fit.