Unkle Al The Artist

Childhood, youth and education

See also: Einstein family

Einstein in 1882, age 3

Albert Einstein was born in Ulm,^[19] in the Kingdom of Württemberg in the German Empire, on 14 March 1879.^[20][21] His parents, secular Ashkenazi Jews, were Hermann Einstein, a salesman and engineer, and Pauline Koch. In 1880, the family moved to Munich's borough of Ludwigsvorstadt-Isarvorstadt, where Einstein's father and his uncle Jakob founded Elektrotechnische Fabrik J. Einstein & Cie, a company that manufactured electrical equipment based on direct current.^[19]

Albert attended St. Peter‘s Catholic elementary school in Munich from the age of five. When he was eight, he was transferred to the Luitpold Gymnasium, where he received advanced primary and then secondary school education.^[22]

In 1894, Hermann and Jakob's company tendered for a contract to install electric lighting in Munich, but without success—they lacked the capital that would have been required to update their technology from direct current to the more efficient, alternating current alternative.^[23] The failure of their bid forced them to sell their Munich factory and search for new opportunities elsewhere. The Einstein family moved to Italy, first to Milan and a few months later to Pavia, where they settled in Palazzo Cornazzani.^[24] Einstein, then fifteen, stayed behind in Munich in order to finish his schooling. His father wanted him to study electrical engineering, but he was a fractious pupil who found the Gymnasium's regimen and teaching methods far from congenial. He later wrote that the school's policy of strict rote learning was harmful to creativity. At the end of December 1894, a letter from a doctor persuaded the Luitpold's authorities to release him from its care, and he joined his family in Pavia.^[25] While in Italy as a teenager, he wrote an essay entitled 

"On the Investigation of the State of the Ether in a Magnetic Field".^[26][27]

Uber die Untersuchung des Aetherzustandes im magnetischen Felde. Nachfolgende Zeilen sind der erste bescheidene Ausdruck einiger einfacher Gedanken über dies schwierige Thema. Mit schwerem Herzen dränge ich dieselben in einen Aufsatz zusammen, der eher wie ein Programm als wie eine Abhandlung aussieht. Weil es mir aber vollständig an Material fehlte, um

Uber die Untersuchung des Aetherzustandes im magnetischen Felde. Nachfolgende Zeilen sind der erste bescheidene Ausdruck einiger einfacher Gedanken über dies schwge Thema. Mit schwerem Herzen dränge ich dieselben in einen Aufsatz zusammen, der eher wie ein Programm als wie eine Abhandlung aussieht. Weil es mir aber vollständig an Material fehlte, um

Einstein excelled at physics and mathematics from an early age, and soon acquired the mathematical expertise normally only found in a child several years his senior. He began teaching himself algebra, calculus and Euclidean geometry when he was twelve; he made such rapid progress that he discovered an original proof of the Pythagorean theorem before his thirteenth birthday.^[28][29][30] A family tutor, Max Talmud, said that only a short time after he had given the twelve year old Einstein a geometry textbook, the boy "had worked through the whole book. He thereupon devoted himself to higher mathematics ... Soon the flight of his mathematical genius was so high I could not follow."^[31] Einstein recorded that he had "mastered integral and differential calculus" while still just fourteen.^[29] His love of algebra and geometry was so great that at twelve, he was already confident that nature could be understood as a "mathematical structure".^[31]

Pythagorean theorem

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From Wikipedia, the free encyclopedia

Proofs using constructed squares

Rearrangement proof of the Pythagorean theorem.

(The area of the white space remains constant throughout the translation rearrangement of the triangles. At all moments in time, the area is always c². And likewise, at all moments in time, the area is always a²+b².)

Pythagorean theorem

Type	Theorem
Field	Euclidean geometry
Statement	The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).
Symbolic statement	${\displaystyle {𝑎}^2+{𝑏}^2={𝑐}^2}$
Generalizations	Law of cosines Solid geometry Non-Euclidean geometry Differential geometry
Consequences	Pythagorean triple Reciprocal Pythagorean theorem Complex number Euclidean distance Pythagorean trigonometric identity