Square-Cube Law
The square-cube law states that as an object scales up by a linear factor, its surface area grows with the square of that factor while its volume grows with the cube. Because heat is generated in proportion to volume but shed through surface area, larger objects overheat more easily — a core reason batteries, engines, and organisms face hard limits on how big they can simply be scaled up.
The square-cube law describes how the geometric properties of an object change as it is scaled. If every linear dimension is multiplied by a factor x, the surface area grows by x squared while the volume grows by x cubed. Volume therefore grows faster than surface area as a shape gets larger. This mismatch has wide consequences. For heat dissipation, internal heat generation typically scales with volume (x cubed) while the surface available to shed that heat scales only with area (x squared), so larger bodies overheat more readily and are harder to cool. This is a central reason a Lithium-Ion Battery is built from many small cells rather than one giant cell, and why the risk of Thermal Runaway rises with cell size. The law also constrains biology and engineering. The bones of an elephant must be proportionately far thicker than those of a mouse because weight (a volume effect) climbs faster than the cross-section of bone supporting it. Aircraft cannot simply be photographically enlarged, since lift depends on wing area but weight scales with volume. Building heights and large pressure vessels run into similar limits. The same r-squared versus r-cubed relationship that governs an elephant's legs governs why you cannot just scale a battery up without it cooking itself in the middle.