1af6e7aa5a
* fix: clean-up Project Euler 321-340 * fix: typo * fix: corrections from review Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
53 lines
1.4 KiB
Markdown
53 lines
1.4 KiB
Markdown
---
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id: 5900f4b91000cf542c50ffcb
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title: 'Problem 332: Spherical triangles'
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challengeType: 5
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forumTopicId: 301990
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dashedName: problem-332-spherical-triangles
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---
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# --description--
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A spherical triangle is a figure formed on the surface of a sphere by three great circular arcs intersecting pairwise in three vertices.
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<img class="img-responsive center-block" alt="spherical triangle formed on the surface of a sphere" src="https://cdn.freecodecamp.org/curriculum/project-euler/spherical-triangles.jpg" style="background-color: white; padding: 10px;">
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Let $C(r)$ be the sphere with the centre (0,0,0) and radius $r$.
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Let $Z(r)$ be the set of points on the surface of $C(r)$ with integer coordinates.
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Let $T(r)$ be the set of spherical triangles with vertices in $Z(r)$. Degenerate spherical triangles, formed by three points on the same great arc, are <u>not</u> included in $T(r)$.
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Let $A(r)$ be the area of the smallest spherical triangle in $T(r)$.
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For example $A(14)$ is 3.294040 rounded to six decimal places.
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Find $\displaystyle \sum_{r = 1}^{50} A(r)$. Give your answer rounded to six decimal places.
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# --hints--
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`sphericalTriangles()` should return `2717.751525`.
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```js
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assert.strictEqual(sphericalTriangles(), 2717.751525);
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```
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# --seed--
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## --seed-contents--
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```js
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function sphericalTriangles() {
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return true;
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}
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sphericalTriangles();
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```
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# --solutions--
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```js
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// solution required
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```
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