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Current theories suggest that on Earth and, possibly, on other terrestrial planets early in their history, the first continental crust may has been produced by direct melting of hydrated peridotite. However, the conditions, mechanisms and…
Gravity plays an important part in the experiments and discoveries of the modern world. But how was it discovered? Surely Newton and Einstein were not the only people to observe it and account for it. It had been a long path before the full…
The conic sections, as well as the solids obtained by revolving these curves, and many of their surprising properties, were already studied by Greek mathematicians since at least the fourth century B.C. Some of these properties come to the…
In his treatise addressed to Dositheus of Pelusium, Archimedes of Syracuse obtained the result of which he was the most proud: a sphere has two-thirds the volume of its circumscribing cylinder. At his request a sculpted sphere and cylinder…
In the 16th century, Simon Stevin initiated a modern approach to decimal representation of measuring numbers, marking a transition from the discrete arithmetic practised by the Greeks to the arithmetic of the continuum taken for granted…
We introduce some classes of genuine higher categories in homotopy type theory, defined as well-behaved subcategories of the category of types. We give several examples, and some techniques for showing other things are not examples. While…
In order to examine how the terrestrial life emerged, a number of laboratory experiments have been conducted since the 1950s. Methane has been one of the key molecules in these studies. In earlier studies, strongly reducing gas mixtures…
Since 1945 Canada has had a nuclear power industry based on reactor design which uses natural uranium and heavy water. The tortuous and improbable sequence of events which led to this situation is examined.
Since its inception at the beginning of the twentieth century, quantum mechanics has challenged our conceptions of how the universe ought to work; however, the equations of quantum mechanics can be too computationally difficult to solve…
Eight decades ago, Arthur Holmes introducted the idea of mantle convection as a mechanism for continental drift. Five decades ago, continental drift was modified to become plate tectonics theory, which included mantle convection as an…
A Platonic surface is a Riemann surface that underlies a regular map and so we can consider its vertices, edge-centres and face-centres. A symmetry (anticonformal involution) of the surface will fix a number of simple closed curves which we…
We describe the construction of a new family of developable rollers based on the Platonic solids. In this way kinetic sculptures may be realised, with the Platonic solids quite literally in their heart. We also describe the strong way in…
Are symmetries discovered or rather invented by humans ? The stand you may take firmly here reveals a lot of your epistemological position. Conversely, the arguments you may forge for answering to this question, or to one of its numerous…
In this chapter we review the astrophysical origins of Earth's carbon, starting from the products of the Big Bang and culminating with the Earth's formation. We review the measured compositions of different primitive objects including…
This article focuses on evolvement of the history of mathematics as a science and development of its methodology from the 4th century B.C. to the age of Enlightenment.
This article will take you on a journey to the core of blockchains, their Byzantine consensus engine, where HotStuff emerged as a new algorithmic foundation for the classical Byzantine generals consensus problem. The first part of the…
Despite being one of the most recognisable buildings from ancient Rome, the Pantheon is poorly understood. While its architecture has been well studied, its function remains uncertain. This paper argues that both the design and the meaning…
Compositionally complex materials have demonstrated extraordinary promise for structural robustness in extreme environments. Of these, the most commonly thought of are high entropy alloys, where chemical complexity grants uncommon…
The pedal of a curve in the Euclidean plane is a classical subject which has a singular point at the inflection point of the original curve or the pedal point. The primitive of a curve is a curve given by the inverse construction for making…
Crochet provides a superior method for the production of two-dimensional surfaces from one-dimensional material. Compared to any of the other known processes to generate constant flat, spherical or hyperbolic shapes, it is the most flexible…