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| Thesis|Thinking on Space Art|Glossary

Glossary for Thinking on Space Art 11

 

Written and translated by Taketoshi Murayama

Original translation is rewritten by Michiko Takahashi Christofis

 


   Palazzo della Signoria

 

Cosimo I de Medici
Cosimo I
def Medici

Palazzo Vecchio
Palazzo Vecchio
Palazzo Pitti
Palazzo Pitti

The building which is used as the seat of the town authorities of Florence. It is called Palazzo Vecchio, too. It was built under the design of Arnolfo di Cambio from 1299 to 1304, facing the " Piazza della Signoria " in the heart of Florence. Cosimo I def Medici (1519-1574) used this building as his residence in the 16th century. Later when the Medici family moved to Palazzo Pitti, it came to be called " Palazzo Vecchio (means old) ", but it was in continual use as the governmental office of the Republic of Florence. When Florence became the capital of the unified Italy kingdom in the 19th century, this building was used as the  Chamber of Deputies and the Foreign Ministry.

da Vinci
Leonardo da Vinci
Michelangelo
Michelangelo
Buonarroti

  This building has two stories, and the clock tower called " the Arnolfo tower " which reaches 94 meters in height. The outward appearance of the building is in the Gothic style, but the interiors are made in the pure Renaissance style. On the second floor, there is " Salone dei Cinquecento ", well known as the cite of mural painting competition between Leonardo da Vinci (1452-1519 Italian artist, scientist) and Michelangelo Buonarroti (1475-1564 Italian space artist).

 

(Written and translated by Taketoshi Murayama. Original translation is rewritten by Michiko Takahashi Christofis)



  The Accademia Gallery

 

Vasari
Giorgio Vasari
Michelangelo
Michelangelo
Buonarroti

In the 18th century, the Lorraine Grand Dukes Pietro Leopoldo established the academy integrating every field of art in Florence, after the model of " Accademia del Disegno " which Giorgio Vasari (1511-1574 Italian painter, architect, biographer) made in the 16th century. During the 19th century, in this academy, a scheme was laid to gather works of old masters and make a museum to serve as teaching materials for students. Then, to mark the fourth centenary of Michelangelo Buonarrotifs (1475-1564 Italian space artist) birth, there was a plan to bring together his works in a hall, but it was not realized for lack of budget. " David ", in front of the Palazzo della Signoria, was transferred with some of his unfinished sculptures such as " Captives " and " Saint Matthew " housed here, in addition to the works of other painters of the Renaissance, at the present-day Accademia Gallery.

 

(Written and translated by Taketoshi Murayama. Original translation is rewritten by Michiko Takahashi Christofis)




 Quadric surface@ Quadratic curve

 

Let's formulate an equation adding up the terms composed of three variables (x, y, z), squares of each variable, the products of every two sets of the variables, each of those being multiplied by an arbitrary coefficient, and a constant to give a sum of zero. A set of points which meet this equation in the three-dimensional coordinates where (x, y, z) are perpendicular to each other form a curved surface called quadric.

In an equation with two variables (x, y,) formulated in the same manner, a quadratic curve appears in the plane represented by the coordinates of x and y. The quadratic curve includes circle, ellipse, parabola, and hyperbola; in the quadric surface, these curves appear in an arbitrary section. When cutting off a cone in some plane, a quadratic curve appears on its section, so this is called conic section as well.

 

(Written and translated by Taketoshi Murayama. Original translation is rewritten by Michiko Takahashi Christofis)



   Cubic function

 

A function expressed by an equation where the sum of the term, composed of an independent variable and its square and cube, each being multiplied by an arbitrary coefficient, added by a constant gives a dependent variable. Generally, this function shows a curve. There are one maximal point and one minimal point where differential calculus coefficient becomes 0, and between them, there is an inflection point at which differential calculus coefficient turns from increase to decrease ( the second derivative becomes 0 ). Also, this function is an odd function and the formed curve is symmetrical to the coordinate origin; the more ( the less ) independent variable, the more ( the less) dependent variable.

(Written and translated by Taketoshi Murayama. Original translation is rewritten by Michiko Takahashi Christofis)


  Trigonometrical function

 

A mathematical expression of the ratio in length between sides of a right-angled triangle in the form of a function of an angle formed between the hypotenuse and the base. In all, there are six kinds in ratio of the length of sides of a right-angled triangle. Among these ratios generally used are: sine, height divided by hypotenuse; cosine, base divided by hypotenuse; tangent, height divided by base. Three kinds of the rest ratios can be expressed by the reciprocals of these. Since tangent is equal to the value of sine divided by cosine, trigonometrical function is eventually represented by sine and cosine.

The horizontal coordinate of a certain point on circumference with radius 1, a center of which is on the coordinate origin, is cosine of an angle formed between the horizontal line and the straight line linking the center and that point, and the perpendicular coordinate is the value of sine of the angle. When moving this point at equal angular velocity on the circumference with radius 1, the change of the value on the horizontal coordinates represents that of cosine; the change of the value on the perpendicular coordinates represents that of sine. Now let the change of the angle be an independent variable, and the value of the change of sine or cosine a dependent variable here, this function shows a simple wave motion curve, repeating with the amplitude of vibration of 1 and the period of 360 degrees. The wave motion of sine and wave motion of cosine are same in shape, but they differ in phase by 90 degrees. The complicated wave motion can be shown as the synthesis of this simple wave motion.

(Written and translated by Taketoshi Murayama. Original translation is rewritten by Michiko Takahashi Christofis)


  Exponential function   Logarithm function

 

Exponential function is a function, in raising a given number to the n-th power, having the number of power as an independent variable and the calculated result as a dependent variable. Logarithm function is the inverse function of exponential function in which an independent variable and a dependent variable are replaced. The number which is powered in exponential function is called a base in logarithm function. Since these two are inverse function to each other, geometrically they form the same curve in shape. Curves of exponential function and logarithm function are symmetrical with a 45-degree straight line as an axis.


(Written and translated by Taketoshi Murayama. Original translation is rewritten by Michiko Takahashi Christofis)



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