De re aedificatoriaDe re aedificatoria (On the Art of Building) is a classic architectural treatise written by Leon Battista Alberti between 1443 and 1452. Although largely dependent on Vitruvius's De architectura, it was the first theoretical book on the subject written in the Italian Renaissance, and in 1485 it became the first printed book on architecture. It was followed in 1486 with the first printed edition of Vitruvius. Alberti's Ten Books consciously echoes Vitruvius's writing, but Alberti also adopts a critical attitude toward his predecessor.
Revivalism (architecture)Architectural revivalism is the use of elements that echo the style of a previous architectural era that have or had fallen into disuse or abeyance between their heyday and period of revival. Revivalism, in a narrower sense, refers to the period of- and movement within- Western architectural history during which a succession of antecedent and remenescent styles were taken to by architects, roughly from the late 18th century, and which was itself succeeded by Modernism.
Symmetry (geometry)In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under the transform). Thus, a symmetry can be thought of as an immunity to change. For instance, a circle rotated about its center will have the same shape and size as the original circle, as all points before and after the transform would be indistinguishable.
Icosahedral symmetryIn mathematics, and especially in geometry, an object has icosahedral symmetry if it has the same symmetries as a regular icosahedron. Examples of other polyhedra with icosahedral symmetry include the regular dodecahedron (the dual of the icosahedron) and the rhombic triacontahedron. Every polyhedron with icosahedral symmetry has 60 rotational (or orientation-preserving) symmetries and 60 orientation-reversing symmetries (that combine a rotation and a reflection), for a total symmetry order of 120.
MathematicsMathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them.
VitruviusVitruvius (vɪˈtruːviəs; c. 80–70 BC – after c. 15 BC) was a Roman architect and engineer during the 1st century BC, known for his multi-volume work titled De architectura. He originated the idea that all buildings should have three attributes: firmitas, utilitas, and venustas ("strength", "utility", and "beauty"). These principles were later widely adopted in Roman architecture. His discussion of perfect proportion in architecture and the human body led to the famous Renaissance drawing of the Vitruvian Man by Leonardo da Vinci.
EllipseIn mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured by its eccentricity , a number ranging from (the limiting case of a circle) to (the limiting case of infinite elongation, no longer an ellipse but a parabola).
AntiprismIn geometry, an n-gonal antiprism or n-antiprism is a polyhedron composed of two parallel direct copies (not mirror images) of an n-sided polygon, connected by an alternating band of 2n triangles. They are represented by the Conway notation An. Antiprisms are a subclass of prismatoids, and are a (degenerate) type of snub polyhedron. Antiprisms are similar to prisms, except that the bases are twisted relatively to each other, and that the side faces (connecting the bases) are 2n triangles, rather than n quadrilaterals.
Power of a pointIn elementary plane geometry, the power of a point is a real number that reflects the relative distance of a given point from a given circle. It was introduced by Jakob Steiner in 1826. Specifically, the power of a point with respect to a circle with center and radius is defined by If is outside the circle, then , if is on the circle, then and if is inside the circle, then . Due to the Pythagorean theorem the number has the simple geometric meanings shown in the diagram: For a point outside the circle is the squared tangential distance of point to the circle .
DodecahedronIn geometry, a dodecahedron (; ) 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.
Mathematics educationIn contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out scholarly research into the transfer of mathematical knowledge. Although research into mathematics education is primarily concerned with the tools, methods, and approaches that facilitate practice or the study of practice, it also covers an extensive field of study encompassing a variety of different concepts, theories and methods.
Radical axisIn Euclidean geometry, the radical axis of two non-concentric circles is the set of points whose power with respect to the circles are equal. For this reason the radical axis is also called the power line or power bisector of the two circles. In detail: For two circles c_1, c_2 with centers M_1, M_2 and radii r_1, r_2 the powers of a point P with respect to the circles are Point P belongs to the radical axis, if If the circles have two points in common, the radical axis is the common secant line of the circles.
