ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
1.2 KiB
1.2 KiB
id, title, challengeType, forumTopicId, dashedName
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f5431000cf542c510056 | Problem 471: Triangle inscribed in ellipse | 5 | 302148 | problem-471-triangle-inscribed-in-ellipse |
--description--
The triangle ΔABC is inscribed in an ellipse with equation \\frac {x^2} {a^2} + \\frac {y^2} {b^2} = 1, 0 < 2b < a, a and b integers.
Let r(a,b) be the radius of the incircle of ΔABC when the incircle has center (2b, 0) and A has coordinates \\left( \\frac a 2, \\frac {\\sqrt 3} 2 b\\right).
For example, r(3,1) = ½, r(6,2) = 1, r(12,3) = 2.
Let G(n) = \\sum*{a=3}^n \\sum*{b=1}^{\\lfloor \\frac {a - 1} 2 \\rfloor} r(a, b) You are given G(10) = 20.59722222, G(100) = 19223.60980 (rounded to 10 significant digits). Find G(1011). Give your answer in scientific notation rounded to 10 significant digits. Use a lowercase e to separate mantissa and exponent. For G(10) the answer would have been 2.059722222e1.
--hints--
euler471() should return 1.895093981e+31.
assert.strictEqual(euler471(), 1.895093981e31);
--seed--
--seed-contents--
function euler471() {
return true;
}
euler471();
--solutions--
// solution required