Golden ratio
Line segments in the golden ratio In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b > 0, The golden ratio is also called the golden section (Latin: sectio aurea) or golden mean.[1][2][3] Other names include extreme and mean ratio,[4] medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut,[5] and golden number.[6][7][8] Some twentieth-century artists and architects, including Le Corbusier and Dalí, have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing (see Applications and observations below). Calculation Therefore, Multiplying by φ gives and History
Immanuel Kant
Immanuel Kant (/kænt/;[1] German: [ɪˈmaːnu̯eːl kant]; 22 April 1724 – 12 February 1804) was a German philosopher who is widely considered to be a central figure of modern philosophy. He argued that fundamental concepts structure human experience, and that reason is the source of morality. His thought continues to have a major influence in contemporary thought, especially the fields of metaphysics, epistemology, ethics, political philosophy, and aesthetics.[2] Kant's major work, the Critique of Pure Reason (Kritik der reinen Vernunft, 1781),[3] aimed to explain the relationship between reason and human experience. Kant argued that our experiences are structured by necessary features of our minds. Kant aimed to resolve disputes between empirical and rationalist approaches. Biography[edit] Immanuel Kant was born in 1724 in Königsberg, Prussia (since 1946 the city of Kaliningrad, Kaliningrad Oblast, Russia). Young Kant was a solid, albeit unspectacular, student. Young scholar[edit] [edit]
Johannes Kepler
Johannes Kepler (German: [ˈkʰɛplɐ]; December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer. A key figure in the 17th century scientific revolution, he is best known for his laws of planetary motion, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astronomy. These works also provided one of the foundations for Isaac Newton's theory of universal gravitation. During his career, Kepler was a mathematics teacher at a seminary school in Graz, Austria, where he became an associate of Prince Hans Ulrich von Eggenberg. Early years[edit] Birthplace of Johannes Kepler in Weil der Stadt The Great Comet of 1577, which Kepler witnessed as a child, attracted the attention of astronomers across Europe. He was introduced to astronomy at an early age, and developed a love for it that would span his entire life. Graz (1594–1600)[edit] Mysterium Cosmographicum[edit] Close-up of inner section of the model Marriage to Barbara Müller[edit]
la jeunesse
Kant's Aesthetics and Teleology
First published Sat Jul 2, 2005; substantive revision Wed Feb 13, 2013 Kant's views on aesthetics and teleology are given their fullest presentation in his Critique of Judgment (Kritik der Urteilskraft, also translated Critique of the Power of Judgment), published in 1790. This work is in two parts, preceded by a long introduction in which Kant explains and defends the work's importance in his critical system overall: in the first part, the “Critique of Aesthetic Judgment,” Kant discusses aesthetic experience and judgment, in particular of the beautiful and the sublime, and also artistic creation; in the second part, the “Critique of Teleological Judgment,” he discusses the role of teleology (that is, appeal to ends, purposes or goals) in natural science and in our understanding of nature more generally. The Critique of Judgment has received less attention than the other two Critiques. 1. 2. Other elements of Kant's theory are sketched in the remainder of the section.
Cymatics a study of Wave Phenomena by Hans Jenny
Friedrich Nietzsche
Friedrich Wilhelm Nietzsche (/ˈniːtʃə/[1] or /ˈniːtʃi/;[2] German: [ˈfʁiːdʁɪç ˈvɪlhɛlm ˈniːt͡sʃə]; 15 October 1844 – 25 August 1900) was a German philosopher, cultural critic, poet, composer and Latin and Greek scholar. He wrote several critical texts on religion, morality, contemporary culture, philosophy and science, displaying a fondness for metaphor[3] and irony. Nietzsche's key ideas include perspectivism, the will to power, the death of God, the Übermensch and eternal recurrence. One of the key tenets of his philosophy is "life-affirmation", which embraces the realities of the world in which we live over the idea of a world beyond. Nietzsche began his career as a classical philologist—a scholar of Greek and Roman textual criticism—before turning to philosophy. As his caretaker, his sister assumed the roles of curator and editor of Nietzsche's manuscripts. Life[edit] Youth (1844–69)[edit] Nietzsche in his younger days In 1866, he read Friedrich Albert Lange's History of Materialism.
Jakob Böhme
Jakob Böhme (/ˈbeɪmə, ˈboʊ-/;[1] 1575 – November 17, 1624) was a German Christian mystic and theologian. He is considered an original thinker within the Lutheran tradition, and his first book, commonly known as Aurora, caused a great scandal. In contemporary English, his name may be spelled Jacob Boehme; in seventeenth-century England it was also spelled Behmen, approximating the contemporary English pronunciation of the German Böhme. Biography[edit] Jakob Böhme (anonymous portrait) Böhme was born in March 8, 1575, at Alt Seidenberg (now Stary Zawidów, Poland), a village near Görlitz in Upper Lusatia, a territory of the Holy Roman Empire. In 1610 Böhme experienced another inner vision in which he further understood the unity of the cosmos and that he had received a special vocation from God. The shop in Görlitz, which was sold in 1613, had allowed Böhme to buy a house in 1610 and to finish paying for it in 1618. Aurora and writings[edit] Theology[edit] 1. 1. Cosmology[edit] Marian views[edit]
plafond
