High surface tension in water
Surface tension
High surface tension in water
Surface tension is a result of the cohesive forces between water molecules, primarily due to hydrogen bonding.
Example
Water striders can walk on water because of its high surface tension, which supports their weight without breaking the surface.
Understanding surface tension helps explain phenomena like water striders' ability to float on water.
Related concepts
List of unsolved problems in mathematics
Random points in high dimensions are nearly equidistant due to the uniform distribution of volume in high-dimensional space
the Lp norm ball shape changes as p goes from 1 to 2 to infinity
As p increases from 1 to 2 to infinity, the Lp norm ball becomes more spherical
the volume of a unit ball approaches zero as dimensions increase
As dimensions increase, the volume of a unit ball approaches zero due to the formula V = (π^(d/2) / Γ(d/2 + 1))^(1/d), where d is the dimension
saddle points are more common than local minima in high dimensions
Saddle points arise due to mixed partial derivatives being zero, leading to more complex curvature in high dimensions
the determinant tells you about volume scaling under a linear transformation
The determinant of a matrix representing a linear transformation indicates the factor by which volumes are scaled
Manifold hypothesis
High-dimensional data lies on lower-dimensional manifolds
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