|
Divina Proportione
''Divina proportione'' (15th century Italian for ''Divine proportion''), later also called ''De divina proportione'' (converting the Italian title into a Latin one) is a book on mathematics written by Luca Pacioli and illustrated by Leonardo da Vinci, completed by February 9th, 1498 in Milan and first printed in 1509. Its subject was mathematical proportions (the title refers to the golden ratio) and their applications to geometry, to visual art through perspective, and to architecture. The clarity of the written material and Leonardo's excellent diagrams helped the book to achieve an impact beyond mathematical circles, popularizing contemporary geometric concepts and images. Some of its content was plagiarised from an earlier book by Piero della Francesca, ''De quinque corporibus regularibus''. Contents of the book The book consists of three separate manuscripts, which Pacioli worked on between 1496 and 1498. He credits Fibonacci as the main source for the mathematics he pre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luca Pacioli
Fra Luca Bartolomeo de Pacioli (sometimes ''Paccioli'' or ''Paciolo''; 1447 – 19 June 1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to the field now known as accounting. He is referred to as the father of accounting and bookkeeping and he was the first person to publish a work on the double-entry system of book-keeping on the continent. He was also called Luca di Borgo after his birthplace, Borgo Sansepolcro, Tuscany. Several of his works were plagiarised from Piero della Francesca, in what has been called "probably the first full-blown case of plagiarism in the history of mathematics". Life Luca Pacioli was born between 1446 and 1448 in the Tuscan town of Sansepolcro where he received an abbaco education. This was education in the vernacular (''i.e.'', the local tongue) rather than Latin and focused on the knowledge required of merchants. His father was Bartolomeo Pacioli; however, Luca Pacioli was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Quinque Corporibus Regularibus
''De quinque corporibus regularibus'' (sometimes called ''Libellus de quinque corporibus regularibus'') is a book on the geometry of polyhedra written in the 1480s or early 1490s by Italian painter and mathematician Piero della Francesca. It is a manuscript, in the Latin language; its title means '' he little bookon the five regular solids''. It is one of three books known to have been written by della Francesca. Along with the Platonic solids, ''De quinque corporibus regularibus'' includes descriptions of five of the thirteen Archimedean solids, and of several other irregular polyhedra coming from architectural applications. It was the first of what would become many books connecting mathematics to art through the construction and perspective drawing of polyhedra, including Luca Pacioli's 1509 ''Divina proportione'' (which incorporated without credit an Italian translation of della Francesca's work). Lost for many years, ''De quinque corporibus regularibus'' was rediscovered i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semiregular Polyhedra
In geometry, the term semiregular polyhedron (or semiregular polytope) is used variously by different authors. Definitions In its original definition, it is a polyhedron with regular polygonal faces, and a symmetry group which is transitive on its vertices; today, this is more commonly referred to as a uniform polyhedron (this follows from Thorold Gosset's 1900 definition of the more general semiregular polytope). These polyhedra include: *The thirteen Archimedean solids. ** The elongated square gyrobicupola, also called a pseudo-rhombicuboctahedron, a Johnson solid, has identical vertex figures 3.4.4.4, but is not vertex-transitive including a twist has been argued for inclusion as a 14th Archimedean solid by Branko Grünbaum. *An infinite series of convex prisms. *An infinite series of convex antiprisms (their semiregular nature was first observed by Kepler). These semiregular solids can be fully specified by a vertex configuration: a listing of the faces by number of sid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Polyhedra
A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equivalent definitions are used; a common one is that the faces are congruent regular polygons which are assembled in the same way around each vertex. A regular polyhedron is identified by its Schläfli symbol of the form , where ''n'' is the number of sides of each face and ''m'' the number of faces meeting at each vertex. There are 5 finite convex regular polyhedra (the Platonic solids), and four regular star polyhedra (the Kepler–Poinsot polyhedra), making nine regular polyhedra in all. In addition, there are five regular compounds of the regular polyhedra. The regular polyhedra There are five convex regular polyhedra, known as the Platonic solids, four regular star polyhedra, the Kepler–Poinsot polyhedra, and five regular compounds ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aether (classical Element)
According to ancient and medieval science, aether (, alternative spellings include ''æther'', ''aither'', and ''ether''), also known as the fifth element or quintessence, is the material that fills the region of the universe beyond the terrestrial sphere. The concept of aether was used in several theories to explain several natural phenomena, such as the traveling of light and gravity. In the late 19th century, physicists postulated that aether permeated all throughout space, providing a medium through which light could travel in a vacuum, but evidence for the presence of such a medium was not found in the Michelson–Morley experiment, and this result has been interpreted as meaning that no such luminiferous aether exists. Mythological origins The word (''aithḗr'') in Homeric Greek means "pure, fresh air" or "clear sky". In Greek mythology, it was thought to be the pure essence that the gods breathed, filling the space where they lived, analogous to the ''air'' breathed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dodecahedron
In geometry, a dodecahedron (Greek , from ''dōdeka'' "twelve" + ''hédra'' "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. There are also three regular star dodecahedra, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120. Some dodecahedra have the same combinatorial structure as the regular dodecahedron (in terms of the graph formed by its vertices and edges), but their pentagonal faces are not regular: The pyritohedron, a common crystal form in pyrite, has pyritohedral symmetry, while the tetartoid has tetrahedral symmetry. The rhombic dodecahedron can be seen as a limiting case of the pyritohedron, and it has octahedral symmetry. The elongated dodecahedron and trapezo-rhombic dodecahedron variations, along with the rhombic dodecahedra, are space-filling. There ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Omnipresence
Omnipresence or ubiquity is the property of being present anywhere and everywhere. The term omnipresence is most often used in a religious context as an attribute of a deity or supreme being, while the term ubiquity is generally used to describe something "existing or being everywhere at the same time, constantly encountered, widespread, common". Ubiquitous can also be used as a synonym for words like worldwide, universal, global, pervasive, all over the place. The omnipresence of a supreme being is conceived differently by different religious systems. In monotheistic beliefs like Christianity and Judaism, the divine and the universe are separate, but the divine is present everywhere. In pantheistic beliefs, the divine and the universe are identical. In panentheistic beliefs, the divine interpenetrates the universe, but extends beyond it in time and space. Introduction Hinduism, and other religions that derive from it, incorporate the theory of ''transcendent and immanent omni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-similarity
__NOTOC__ In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of fractals. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape. The non-trivial similarity evident in fractals is distinguished by their fine structure, or detail on arbitrarily small scales. As a counterexample, whereas any portion of a straight line may resemble the whole, further detail is not revealed. A time developing phenomenon is said to exhibit self-similarity if the numerical v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Irrational Number
In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being '' incommensurable'', meaning that they share no "measure" in common, that is, there is no length ("the measure"), no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself. Among irrational numbers are the ratio of a circle's circumference to its diameter, Euler's number ''e'', the golden ratio ''φ'', and the square root of two. In fact, all square roots of natural numbers, other than of perfect squares, are irrational. Like all real numbers, irrational numbers can be expressed in positional notation, notably as a decimal number. In the cas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Holy Trinity
The Christian doctrine of the Trinity (, from 'threefold') is the central dogma concerning the nature of God in most Christian churches, which defines one God existing in three coequal, coeternal, consubstantial divine persons: God the Father, God the Son (Jesus Christ) and God the Holy Spirit, three distinct persons sharing one ''homoousion'' (essence) "each is God, complete and whole." As the Fourth Lateran Council declared, it is the Father who begets, the Son who is begotten, and the Holy Spirit who proceeds. In this context, the three persons define God is, while the one essence defines God is. This expresses at once their distinction and their indissoluble unity. Thus, the entire process of creation and grace is viewed as a single shared action of the three divine persons, in which each person manifests the attributes unique to them in the Trinity, thereby proving that everything comes "from the Father," "through the Son," and "in the Holy Spirit." This doctrine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divine Simplicity
In theology, the doctrine of divine simplicity says that God is simple (without parts). The general idea can be stated in this way: The being of God is identical to the "attributes" of God. Characteristics such as omnipresence, goodness, truth, eternity, etc., are identical to God's being, not qualities that make up that being as a collection, nor abstract entities inhering in God as in a substance; in other words, one can say that in God both essence and existence are one and the same. This is not to say that God is a simpleton or "simple" to understand. As Peter Weigel states, "Divine simplicity is central to the classical Western concept of God. Simplicity denies any physical or metaphysical composition in the divine being. This means God is the divine nature itself and has no accidents (properties that are not necessary) accruing to his nature. There are no real divisions or distinctions in this nature. Thus, the entirety of God is whatever is attributed to him. Divine si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.webp/589px-I_xdNnw4OsAgdoyKGlW1lMXwWuG1BwdvSFfHX5HW4Bc_(1).webp.png "Click for more on -> Divine Simplicity")