Uploaded May 2026 | Updated September 2026, 1 week ago
There's a shape you can fill with paint but never finish painting the outside. Take y = 1/x for x ≥ 1, rotate it around the x-axis, and you get Gabriel's Horn — a trumpet stretching to infinity.
The volume? Exactly π cubic units. Finite. But the surface area? Infinite. You could fill the inside with a finite amount of paint, but you'd need an infinite amount to coat the outside.
The thing that holds the paint has less capacity than what it takes to cover it. Not a logical paradox — the math is consistent — but it sure feels like one.
#shorts #math #mathematics
There's a shape you can fill with paint but never finish painting the outside. Take y = 1/x for x ≥ 1, rotate it around the x-axis, and you get Gabriel's Horn — a trumpet stretching to infinity.
The volume? Exactly π cubic units. Finite. But the surface area? Infinite. You could fill the inside with a finite amount of paint, but you'd need an infinite amount to coat the outside.
The thing that holds the paint has less capacity than what it takes to cover it. Not a logical paradox — the math is consistent — but it sure feels like one.
#shorts #math #mathematics
