正五边形和五角星为什么离不开黄金比？
Why are the regular pentagon and pentagram tied to the golden ratio?
正五边形对角线与边长之比正是 φ=(1+√5)/2；五角星里层层嵌套的小五角星也保持同一比例，形成自相似。这是五重对称与 φ 的内在联系。
In a regular pentagon the diagonal-to-side ratio is φ=(1+√5)/2; the pentagram nests smaller pentagrams at the same ratio, self-similar. This links fivefold symmetry to φ.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Courant & Robbins,《What Is Mathematics?》Oxford University Press,1996 第二版;中译《什么是数学》
R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, 1996; Chinese ed.
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL811195W：What is mathematics?（按标题
#黄金比 #对称
斐波那契数还能用来做‘高效搜索’吗？
Can Fibonacci numbers be used for 'efficient search'?
可以。斐波那契查找用黄金比分割有序数组，每次按斐波那契数比例切分，避免二分查找的乘法，更适合某些硬件。这是数列的工程妙用。
Yes. Fibonacci search splits a sorted array by golden-ratio-like Fibonacci proportions, avoiding the multiplication of binary search and suiting some hardware. A neat engineering use of the sequence.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Courant & Robbins,《What Is Mathematics?》Oxford University Press,1996 第二版;中译《什么是数学》
R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, 1996; Chinese ed.
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL811195W：What is mathematics?（按标题
#黄金比 #算法
斐波那契数列和黄金比有什么关系？
What is the link between Fibonacci numbers and the golden ratio?
斐波那契数列 1,1,2,3,5,8,… 相邻两项之比会趋近于 φ=(1+√5)/2≈1.618，即黄金比。许多植物生长（花瓣、松果）都近似遵循它。
The Fibonacci sequence 1,1,2,3,5,8,… has consecutive ratios converging to φ=(1+√5)/2≈1.618, the golden ratio. Many plant growths (petals, pinecones) approximate it.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Courant & Robbins,《What Is Mathematics?》Oxford University Press,1996 第二版;中译《什么是数学》
R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, 1996; Chinese ed.
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL811195W：What is mathematics?（按标题
#黄金比 #斐波那契