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Its volume would be multiplied by the cube of 2 and become 8 m 3. The original cube (1 m sides) has a surface area to volume ratio of 6:1. The larger (2 m sides) cube has a surface area to volume ratio of (24/8) 3:1. As the dimensions increase, the volume will continue to grow faster than the surface area. Thus the square–cube law.
A 9-cube is a nine-dimensional hypercube with 512 vertices and 18 8-cubes as faces. Learn about its properties, projections, derived polytopes, and references from this Wikipedia article.
Learn about the origins and solutions of cubic equations, which are equations of the form ax3 + bx2 + cx + d = 0. Find out how ancient and medieval mathematicians from different cultures approached and solved cubic equations using algebra, geometry, and numerical approximations.
A cube of a number is its third power, the result of multiplying three instances of the number together. Learn about the cube function, the cube root, the cubic parabola, and the perfect cubes in integers and base ten.
The inverse-square law states that the intensity of a physical quantity is inversely proportional to the square of the distance from the source. Learn how this law applies to gravitation, electrostatics, light, and other phenomena, and see the formula and justification.
A tesseract or 4-cube is a four-dimensional analogue of a cube and a square, with eight cubical cells, 24 square faces, and 32 edges. Learn about its geometry, coordinates, nets, construction, and properties from this comprehensive Wikipedia article.
A cube root of a number x is a number y such that y3 = x. Learn how to find cube roots of real and complex numbers, their geometric and algebraic representations, and their applications in mathematics and geometry.
The Basel problem is a mathematical problem about the sum of the reciprocals of the squares of the natural numbers. It is related to the Riemann zeta function, which has the value pi^2/6 at s = 2. Learn about Euler's solution, generalizations, and applications.