query: Validity of proof for surface area of a sphere
positive_passages.docid: 5086
positive_passages.text: Why is the derivative of a circle's area its perimeter (and similarly for spheres)?
negative_passages.docid: 51877
negative_passages.text: Why is this 'Proof' by induction not valid?
negative_passages.docid: 41651
negative_passages.text: Volume bounded by a sphere of radius $1$ in 4 dimensions
negative_passages.docid: 39015
negative_passages.text: Prove the triangle inequality on the sphere $S^2$ in $\mathbb{R}^3$.
negative_passages.docid: 109174
negative_passages.text: Why is surface charge distribution uniform for a conducting sphere? Can't it be arbitrary?
negative_passages.docid: 60495
negative_passages.text: How to generate uniformly distributed points on the surface of the 3-d unit sphere?
negative_passages.docid: 81748
negative_passages.text: Arc length parameterization lying on a sphere
negative_passages.docid: 66185
negative_passages.text: condition for curve on a sphere
negative_passages.docid: 127248
negative_passages.text: Norm and unit sphere
negative_passages.docid: 14799
negative_passages.text: How to show that the spherical metric satisfies the triangle inequality?
negative_passages.docid: 83449
negative_passages.text: Proof with 3D vectors
negative_passages.docid: 158162
negative_passages.text: Finding the volume of the tetrahedron.
negative_passages.docid: 115677
negative_passages.text: Prove the equality of circle's areas
negative_passages.docid: 118577
negative_passages.text: Fallacious proof involving trigonometry
negative_passages.docid: 82126
negative_passages.text: Volume of bounded region between sphere and a plane
negative_passages.docid: 123742
negative_passages.text: Proving connectedness of the $n$-sphere
negative_passages.docid: 43319
negative_passages.text: Surface area inside cylinder