# Questions tagged [spherical-trigonometry]

For geometric questions about solving spherical triangles and spherical polygons on spheres.

205 questions
Filter by
Sorted by
Tagged with
15 views

### “Diameter” of a sphere [closed]

A sphere is on a table. At a height of 5cm from the table's surface is the sphere center, i.e. the sphere diameter is 10cm. What is it "diameter" at a height of, say, 4cm from the table's ...
42 views

### Determining the lune angles of a spherical quadrilateral

Suppose that we have a convex spherical quadrilateral, and we know its internal angles $\alpha,\beta,\gamma$ and $\delta$. Pairs of opposite sides of the quadrilateral are pieces of distinct great ...
21 views

### Dihedral in a regular spherical polygon

Planes rotate around a central symmetry axis pass through a sphere centre to intersect on the sphere forming a regular spherical polygon of $n$ sides. A small circle forms as base of cone semi-...
36 views

### Manipulating the product of the dot product of multiple vectors is producing a paradox

Unless otherwise indicated all defined vectors lie on the surface of the unit sphere (i.e their norm is 1). Let's take the following expression: $(V\cdot Z_1)(V\cdot Z_2) = V^TZ_1V^TZ_2$ Given that ...
20 views

### Stewart theorem validity on a sphere

EDIT1: On a spherical surface radius $R$ a geodesic triangle is drawn: Let a,b, and c be the lengths of the sides of the geodesic triangle. Let d be the geodesic arc length of a cevian to the side ...
24 views

### Calculus I - Ballon Variation when perforated by a needle

A spherical balance is pierced by a needle so that its volume comes to decrease a rate of $50\, \mathrm{cm}^3 / \mathrm{min}$. Determine an index of variation of your surface area on the moment when ...
28 views

60 views

41 views