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fix: Proofread Part Hotel (3D integrals of scalar functions) - #87

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Jun 19, 2026
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Closes #64.

Proofread the five files of Part Hotel (src/triple.typ, src/sph.typ, src/psurf.typ, src/scalint.typ, src/surfcross.typ). Found and fixed the following small issues:

  • src/triple.typ: comma splice fixed to a period before "In general, given a mass $m$ at a point $O$..." in the gravity section.
  • src/sph.typ: in the algebraic proof of the "illegal angle less than zero" case, the equations used $theta pm phi$ where they should use $theta pm pi$ (the explanation immediately below already correctly refers to $theta pm pi$, so this was an inconsistency).
  • src/sph.typ: "the surface of the sphere are those points" → "is those points" (subject-verb agreement).
  • src/sph.typ: the conclusion of the offset-sphere example called the region $cal(R)$ (should be $cal(T)$, matching the rest of the example) and "polar coordinates" (should be "spherical coordinates", since the answer is given in terms of $rho, phi, theta$).
  • src/psurf.typ: the figure caption for the spherical-Earth parametrization dropped a factor of $sin phi$ in the $y$-component, writing $(sin phi cos theta, phi sin theta, cos phi)$ instead of $(sin phi cos theta, sin phi sin theta, cos phi)$ as defined just above.
  • src/surfcross.typ: in deriving the magic cross-product formula for graphs, the middle component of $partial bf(r)/partial x$ was written as $partial z/partial x$ twice instead of $partial y/partial x$ then $partial z/partial x$.

No large mathematical errors were found; src/scalint.typ checked out with no issues.

🤖 Generated with Claude Code


Generated by Claude Code

Fixes several small typos and calculation errors found while
proofreading Part Hotel:

- triple.typ: comma splice fixed to period before "In general, ..."
- sph.typ: algebraic proof used theta +/- phi instead of theta +/- pi
  for the second illegal-angle case, inconsistent with the
  explanation just below it
- sph.typ: "the surface ... are" -> "is" (subject-verb agreement)
- sph.typ: offset-sphere conclusion referred to T as R and called
  spherical coordinates "polar coordinates"
- psurf.typ: figure caption dropped a factor of sin(phi) in the
  y-component of the spherical parametrization
- surfcross.typ: middle vector component for d(r)/dx was duplicated
  as partial z / partial x instead of partial y / partial x

Closes #64
@vEnhance
vEnhance merged commit a5bf483 into main Jun 19, 2026
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@vEnhance vEnhance added the proofreading-campaign Systematically proofread the textbook label Jun 19, 2026
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Proofread Part Hotel

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