SCIENTIFICAMERICAN  |  Math

Math’s Block-Stacking Problem Has a Preposterous Solution

数学的块堆叠问题有一个荒谬的解决方案

Graphic shows eight multicolored Jenga blocks stacked on a table and oriented perpendicular to the edge. From top to bottom, the blocks extend into space by decreasing proportions of their length.

Graphic shows eight multicolored Jenga blocks stacked on a table and oriented perpendicular to the edge. From top to bottom, the blocks extend into space by decreasing proportions of their length.

2025-07-06  1409  困难
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Don’t click “checkout” on an infinite pack of Jenga blocks just yet. Real-world practicalities such as irregular block shapes, air currents and the crushing weight of an endless edifice may hamper your engineering aspirations. Still, understanding why the overhang has no limit in an ideal mathematical world is enlightening. The explanation hinges on math’s harmonic series and the physics concept of center of mass, two seemingly simple ideas with outsize power. [For more fun, check out: How Tall Can You Build a Tower without It Toppling?]

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