HMMT 十一月 2012 · 冲刺赛 · 第 35 题
HMMT November 2012 — Guts Round — Problem 35
题目详情
英文原题
- [ 20 ] A regular 2012-gon has a circumcircle with radius 1. Compute the area of the 2012-gon. Yourk 2
score will be min(20 , ⌊ ⌋ ), where k is the number of consecutive correct digits immediately followingthe decimal point of your answer.5
解析
英文解析
- [ 20 ]
Answer: 3.1415875473 The answer is 1006 sin . Approximating directly by π = 3 . 1415 . . . isπ
1006
worth only 3 points.
x 3
Using the third-degree Taylor polynomial for sin we can approximate sin x ≈ x − . This gives ananswer of 3 . 1415875473 worth full points. If during the calculation we use the approximation π ≈ 30,36
this gives an answer worth 9 points.
Guts Round