How to lie using visual proofs

Summary by Krater

The video examines three flawed mathematical proofs to illustrate why visual intuition alone is insufficient and why mathematical rigor is necessary.

From the video

Answers: Why are some visual mathematical proofs misleading?

• sphere surface area formula
• proof that pi equals four
• proof that all triangles are isosceles
• mathematical rigor
• limits in calculus

What it concludes

• The surface area of a sphere calculated by unrolling wedge slices yields pi squared r squared, which is false because the true formula is 4 pi r squared.
• Approximating a circle's circumference by folding square corners yields a perimeter of 8, demonstrating that the limit of a sequence of perimeters does not equal the perimeter of the limit curve.
• A geometric proof claiming all triangles are isosceles fails because it relies on the hidden false assumption that intersection points lie inside the triangle.