蜂巢为什么是六边形的?三角形、正方形和圆形谁更结实?
Why are honeycombs hexagons — which shape is strongest: triangles, squares, or circles?
蜜蜂是精打细算的建筑师:六边形能用最少的蜡围出最大的空间,而且彼此严丝合缝不留空隙。承重方面三角形最稳,一压就散的是没有斜撑的正方形;桥梁钢架里全是三角形的身影。形状选择是数学与工程的联手决策。
Bees are thrifty architects: hexagons enclose maximum space with minimum wax and tile together without gaps. For strength, triangles rule — plain squares fold under pressure, which is why bridges brim with steel triangles. Shape choice teams math with engineering.
难度 进阶 · 适合 小学低段(6-8)
CC BY 4.0 · 已核验 · Verified 2026-11-02
来源 · Source
《数学花园漫游记》,马希文,中国少年儿童出版社,2004
Ma Xiwen, Adventures in the Math Garden, China Children Press, 2004
独立核验依据 · Independent verification: 核验依据 1 ISBN 9787500767558（豆瓣书目条目: 数学花园漫游记）
#六边形 #结构强度 #工程数学
什么是角，锐角和钝角有什么不同？
What is an angle, and how do sharp and wide angles differ?
两条直线相遇的地方叫角。比直角尖、张得小的叫锐角；比直角宽、张得大的叫钝角。
An angle is where two lines meet. A sharp, narrow one smaller than a right angle is acute; a wide one bigger than a right angle is obtuse.
难度 入门 · 适合 小学低段(6-8)
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
#角 #锐角
为什么轮子要做成圆的？
Why are wheels made round?
圆圆的轮子转起来时，车离地面的高度一直一样，所以坐车不会一颠一颠。方轮子转起来会上下跳，坐着很难受。
A round wheel stays the same distance from the ground as it turns, so the ride is smooth. A square wheel would bump up and down and feel awful.
难度 入门 · 适合 幼儿(3-6)
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
#圆 #轮子
什么是镶嵌（密铺）？
What is tessellation?
镶嵌是用一种形状不重叠、不露缝地把平面铺满，像地砖。三角形、正方形和六边形都能漂亮地镶嵌，圆形却不行。
Tessellation is covering a flat surface with one shape, no overlaps and no gaps, like floor tiles. Triangles, squares and hexagons tessellate nicely, but circles cannot.
难度 入门 · 适合 小学高段(9-12)
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
#镶嵌 #密铺
为什么球能滚来滚去？
Why can a ball roll around?
球是圆的，每一点离中心都一样远，所以朝哪边推它都能顺利转。方盒子只有边能碰地，就没法顺畅滚动。
A ball is round, with every point equally far from the center, so it turns smoothly in any direction. A box only touches the ground on its edges, so it cannot roll well.
难度 入门 · 适合 小学低段(6-8)
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
#球 #圆
为什么镜子里的我左右反了？
Why does a mirror flip me left-right?
镜子其实是把前后反过来，不是左右。因为我们习惯用“左右”来说话，看起来就像左右对换了。
A mirror actually flips front and back, not left and right. Because we describe things as left-right, it looks like our sides swapped.
难度 入门 · 适合 小学低段(6-8)
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
#对称 #镜子
为什么金字塔要做成三角形侧面？
Why do pyramids have triangular sides?
三角形的侧面能把重量稳稳传向底边，不容易塌。古人发现这种形状又结实又省料，就用来建大金字塔。
Triangular sides carry weight safely down to the base and resist collapse. Ancient builders found this shape strong and efficient, so they used it for great pyramids.
难度 入门 · 适合 小学高段(9-12)
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
#三角形 #金字塔
什么是立体图形，和平面图形有什么不同？
What are 3D shapes and how do they differ from flat ones?
平面图形只有长和宽，像画在纸上的圆；立体图形还有高，像能拿在手里的球。立体图形占了真实的空间，能装东西。
Flat shapes have only length and width, like a circle drawn on paper. Solid shapes also have height, like a ball you can hold. Solids take up real space and can hold things.
难度 入门 · 适合 小学高段(9-12)
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
#立体图形 #平面图形
正方形和长方形有什么不一样？
What is the difference between a square and a rectangle?
正方形四条边一样长，长方形只是对面两边一样长。长方形更像被拉长的正方形。
A square has four equal sides; a rectangle just has equal opposite sides. A rectangle is like a stretched-out square.
难度 入门 · 适合 幼儿(3-6)
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
#正方形 #长方形
为什么圆没有角却最省材料？
Why does a circle save the most material though it has no corners?
用同样长的边围地，圆能圈出最大的面积，所以罐头做成圆的最省铁皮。方形的角会“浪费”一点边能圈到的空间。
With the same length of edge, a circle encloses the most area, so round cans save the most metal. Square corners waste a bit of the space the edge could cover.
难度 入门 · 适合 小学高段(9-12)
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
#圆 #面积
为什么三角形是最稳的平面形状？
Why is the triangle the most stable flat shape?
三条边长度定下来，三角形的样子就完全固定，不会再变形。四边形边长固定还能被压成菱形，所以三角形常被用来加固。
Once a triangle's three side lengths are set, its shape is locked and cannot change. A four-sided shape with fixed sides can still be squashed into a rhombus, so triangles are used to brace things.
难度 入门 · 适合 小学高段(9-12)
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
#三角形 #稳定
为什么积木有的是方的、有的是圆的？
Why are some blocks square and some round?
方积木能稳稳叠高，圆积木会滚来滚去。不同形状有不同的本事，所以玩具盒里常两种都有。
Square blocks stack steady, while round ones roll away. Different shapes have different talents, so toy boxes often have both.
难度 入门 · 适合 幼儿(3-6)
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
#形状 #积木
为什么正方体盒子好叠放？
Why do cube boxes stack well?
正方体的六个面都是一样大的正方形，平平的能稳稳叠在一起。圆球会到处滚，就不好堆。
A cube has six equal square faces that sit flat, so boxes stack steadily. Round balls roll away and are hard to pile up.
难度 入门 · 适合 小学低段(6-8)
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
#正方体 #堆叠
为什么车轮、披萨和月亮都是圆形的?
Why are wheels, pizzas, and the moon all round?
圆非常特别:边上每个点到中心的距离都一样远,所以轮子转起来不颠簸,披萨切出来每块都公平。月亮那么大,引力把它拉成圆球,所以也是圆的。在家玩寻宝游戏:找出十个圆形宝贝,圆就是形状世界冠军!
The circle is special: every edge point sits equally far from the center, so wheels roll smoothly and pizza slices come out fair. The moon is so big that gravity pulls it into a round ball, so it is round too. Play a treasure hunt at home: find ten round things and crown circles the world champion.
难度 入门 · 适合 幼儿(3-6)
CC BY 4.0 · 已核验 · Verified 2026-11-02
来源 · Source
《数学花园漫游记》,马希文,中国少年儿童出版社,2004
Ma Xiwen, Adventures in the Math Garden, China Children Press, 2004
独立核验依据 · Independent verification: 核验依据 1 ISBN 9787500767558（豆瓣书目条目: 数学花园漫游记）
#圆形 #观察 #生活中的数学