AI Tutor
Look at almost any standard classroom world map, and Greenland appears as colossal as the entire continent of Africa.
In reality, Africa is roughly 14 times larger than Greenland. So why does our map make them look identical in size?
How can a map that distorts continent sizes so wildly still be the world standard for navigation?

The Cylinder Around Earth

To flatten a sphere, cartographers often wrap a flat sheet around the equator to form a tangent cylinder.
On a spherical globe of radius RR, lines of latitudeβ€”called parallelsβ€”shrink as you move toward either pole.
What happens when we unroll that cylinder and force those shrinking rings of latitude into straight, equal lines?

Horizontal Stretching

On a globe, the circumference of a parallel at latitude Ο•\phi is 2Ο€Rcos⁑ϕ2\pi R \cos\phi, but the cylinder forces every parallel to stretch out to the equator's full length, 2Ο€R2\pi R.
The horizontal scale factor khk_h is the stretched length divided by the true length: 2Ο€R2Ο€Rcos⁑ϕ=1cos⁑ϕ\frac{2\pi R}{2\pi R \cos\phi} = \frac{1}{\cos\phi}.
The secant function, written as sec⁑ϕ\sec\phi, is simply defined as 1cos⁑ϕ\frac{1}{\cos\phi}. So the horizontal stretch is exactly sec⁑ϕ\sec\phi.