The discussion begins with a demonstration of the reasons that a large structure proportioned in exactly the same way as a smaller one must necessarily be weaker known as the square-cube law.

Aerospike engines do not suffer from the same limitations because the linear shape of the engine is not subject to the square-cube law.

In it, he discusses the square-cube law, the law of falling bodies and infinity.

The square-cube law also complicates the scaling relationships involved.

The square-cube law – common in many engineering calculations – is expected to be critical to the orbital airship design.

Sports physiologists have attributed the advantage that small stature holds in cycling up steep ascents to the way in which body mass and body surface area scale according to height ( see square-cube law ).

* The square-cube law in aircraft design

Many of his examples are based on the square-cube law, although he does not use that terminology.

Isometric scaling is governed by the square-cube law.

The square-cube law was first mentioned in Two New Sciences ( 1638 ).

The square-cube law can be stated as follows:

Because of the necessary phase change, the expander cycle is thrust limited by the square-cube rule.

In, for example, a Boeing 737 these relationships seem much more ' proportional ', but designing an A380 sized aircraft by merely magnifying the design dimensions of a 737, would result in wings that are too small for the aircraft weight, because of the square-cube rule.

However, since for example the product of a square and a cube would be expressed, in words rather than in numbers, as a square-cube, the numerical property of adding exponents was not clear.

It became the sole `` subject '' of `` international law '' ( a term which, it is pertinent to remember, was coined by Bentham ), a body of legal principle which by and large was made up of what Western nations could do in the world arena.

The enormous changes in world politics have, however, thrown it into confusion, so much so that it is safe to say that all international law is now in need of reexamination and clarification in light of the social conditions of the present era.

To him, law is the command of the sovereign ( the English monarch ) who personifies the power of the nation, while sovereignty is the power to make law -- i.e., to prevail over internal groups and to be free from the commands of other sovereigns in other nations.

Moreover, the law of the land is not irrevocable ; ;

That is to say Gabriel's fundamental law had been so much modified by this time that it was neither fundamental nor law any more.

It is a weakness of Gabriel's analysis that he never seems to realize that his so-called fundamental law had already been cut loose from its foundations when it was adapted to democracy.

Mr. Stavropoulos is the U.N. legal chief and a very good man, but he is not fully versed on some technical points of American law ''.

His father was a professor at Hartford Theological Seminary, and from him he acquired a conviction, which he passed along to me, that there is in the universe of persons a moral law, the law of love, which is a natural law in the same sense as is the physical law.

Since 1918 it has been known that the law of conservation of energy is the direct mathematical consequence of the translational symmetry of the quantity conjugate to energy, namely time.

General equilibrium theory has demonstrated, with varying degrees of mathematical rigor over time, that under certain conditions of competition, the law of supply and demand predominates in this ideal free and competitive market, influencing prices toward an equilibrium that balances the demands for the products against the supplies.

As invoked in everyday life, the " law " usually reflects bad statistics or wishful thinking rather than any mathematical principle.

Although the existence of molecules has been accepted by many chemists since the early 19th century as a result of Dalton's laws of Definite and Multiple Proportions ( 1803 – 1808 ) and Avogadro's law ( 1811 ), there was some resistance among positivists and physicists such as Mach, Boltzmann, Maxwell, and Gibbs, who saw molecules merely as convenient mathematical constructs.

The mathematical form of the Lorentz force law also appeared in this paper.

Newton's three laws of motion, along with his law of universal gravitation, explain Kepler's laws of planetary motion, which were the first to accurately provide a mathematical model or understanding orbiting bodies in outer space.

" And while the conjecture may one day be solved, the argument applies to similar unsolved problems ; to Brouwer, the law of the excluded middle was tantamount to assuming that every mathematical problem has a solution.

Two representative mathematical results describing such patterns are the law of large numbers and the central limit theorem.

A power law is a mathematical relationship between two quantities.

* Hooke's law, for the mathematical model of certain processes

His laws of motion were to be the solid foundation of mechanics ; his law of universal gravitation combined terrestrial and celestial mechanics into one great system that seemed to be able to describe the whole world in mathematical formulae.

As a Neoplatonist philosopher, she belonged to the mathematic tradition of the Academy of Athens, as represented by Eudoxus of Cnidus ; she was of the intellectual school of the 3rd century thinker Plotinus, which encouraged logic and mathematical study in place of empirical enquiry and strongly encouraged law in place of nature.

The inverse square law of interactions mediated by massless bosons is the mathematical consequence of the 3-dimensionality of space.

Full-blooded Platonism is a modern variation of Platonism, which is in reaction to the fact that different sets of mathematical entities can be proven to exist depending on the axioms and inference rules employed ( for instance, the law of the excluded middle, and the axiom of choice ).

As a mathematical equation, Boyle's law is:

Wren's challenge to Halley and Hooke, for the reward of a book worth thirty shillings, was to provide, within the context of Hooke's hypothesis, a mathematical theory linking the Kepler's laws with a specific force law.

Newton's laws of motion, together with his law of universal gravitation and the mathematical techniques of calculus, provided for the first time a unified quantitative explanation for a wide range of physical phenomena.

She comes to understand chaos theory and theorizes the second law of thermodynamics, before either is officially recognized and established in mathematical and scientific communities.

Further scientific and mathematical concepts covered in Arcadia are the second law of thermodynamics, and in relation to it, entropy.

* 1607 – Galileo Galilei arrives a mathematical formulation of the law of falling objects based on his earlier experiments.

* Power law, a general mathematical form for " heavy-tailed " distributions, with a polynomial density function.

In addition to the difficulty of quantifying the " value " of a network, the mathematical justification for Metcalfe's law measures only the potential number of contacts, i. e., the technological side of a network.

In mathematical form, Faraday's law states that:

As with other scientific knowledge, they do not have absolute certainty like mathematical theorems or identities, and it is always possible for a law to be overturned by future observations.

Although the concepts of a law or principle in nature is borderline to philosophy, and presents the depth to which mathematics can describe nature, scientific laws are considered from a scientific perspective and follow the scientific method ; they " serve their purpose " rather than " questioning reality " ( philosophical ) or " statements of logical absolution " ( mathematical ).