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Potato paradox. The potato paradox is a mathematical calculation that has a counter-intuitive result. The Universal Book of Mathematics states the problem as such: [ 1] Fred brings home 100 kg of potatoes, which (being purely mathematical potatoes) consist of 99% water (being purely mathematical water). He then leaves them outside overnight so ...
[2] [3]: 19–21 [4] [5] The basic premise had already been demonstrated by Italian experimenters a few decades earlier. According to the story, Galileo discovered through this experiment that the objects fell with the same acceleration, proving his prediction true, while at the same time disproving Aristotle 's theory of gravity (which states ...
Specific weight. The specific weight, also known as the unit weight (symbol γ, the Greek letter gamma ), is a volume-specific quantity defined as the weight per unit volume of a material. A commonly used value is the specific weight of water on Earth at 4 °C (39 °F), which is 9.807 kilonewtons per cubic metre or 62.43 pounds-force per cubic ...
Pressure in water and air. Pascal's law applies for fluids. Pascal's principle is defined as: A change in pressure at any point in an enclosed incompressible fluid at rest is transmitted equally and undiminished to all points in all directions throughout the fluid, and the force due to the pressure acts at right angles to the enclosing walls.
G. H. Hardy, A Mathematician's Apology (1940) He [Russell] said once, after some contact with the Chinese language, that he was horrified to find that the language of Principia Mathematica was an Indo-European one. John Edensor Littlewood, Littlewood's Miscellany (1986) The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by ...
In his research, Archimedes discovered that an object is buoyed up by a force equal to the weight of the water displaced by the object. In other words, an inflatable boat that displaces 100 pounds (45 kilograms) of water is supported by the same amount of force. An object that floats in a fluid is known as being positively buoyant.
Density ( volumetric mass density or specific mass) is a substance's mass per unit of volume. The symbol most often used for density is ρ (the lower case Greek letter rho ), although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume: [ 1] where ρ is the density, m is the mass, and V is the volume.
The computation of (1 + iπ / N ) N is displayed as the combined effect of N repeated multiplications in the complex plane, with the final point being the actual value of (1 + iπ / N ) N. It can be seen that as N gets larger (1 + iπ / N ) N approaches a limit of −1. Fundamentally, Euler's identity asserts that is equal ...