The problem: Answer a question about this article:
According to Vitruvius, the architect should strive to fulfill each of these three attributes as well as possible. Leon Battista Alberti, who elaborates on the ideas of Vitruvius in his treatise, De Re Aedificatoria, saw beauty primarily as a matter of proportion, although ornament also played a part. For Alberti, the rules of proportion were those that governed the idealised human figure, the Golden mean. The most important aspect of beauty was therefore an inherent part of an object, rather than something applied superficially; and was based on universal, recognisable truths. The notion of style in the arts was not developed until the 16th century, with the writing of Vasari: by the 18th century, his Lives of the Most Excellent Painters, Sculptors, and Architects had been translated into Italian, French, Spanish and English.
Who wrote Lives of the Most Excellent Painters, Sculptors, and Architects?
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The answer: Vasari


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From September 1823 to 1826 Chopin attended the Warsaw Lyceum, where he received organ lessons from the Czech musician Wilhelm Würfel during his first year. In the autumn of 1826 he began a three-year course under the Silesian composer Józef Elsner at the Warsaw Conservatory, studying music theory, figured bass and composition.[n 3] Throughout this period he continued to compose and to give recitals in concerts and salons in Warsaw. He was engaged by the inventors of a mechanical organ, the "eolomelodicon", and on this instrument in May 1825 he performed his own improvisation and part of a concerto by Moscheles. The success of this concert led to an invitation to give a similar recital on the instrument before Tsar Alexander I, who was visiting Warsaw; the Tsar presented him with a diamond ring. At a subsequent eolomelodicon concert on 10 June 1825, Chopin performed his Rondo Op. 1. This was the first of his works to be commercially published and earned him his first mention in the foreign press, when the Leipzig Allgemeine Musikalische Zeitung praised his "wealth of musical ideas".
What was the name of the teacher of Chopin's three year course that began in the fall of 1826?
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The answer: Józef Elsner


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The majority of Sicilians preferred independence to the Savoia kingdom; in 1866, Palermo became the seat of a week-long popular rebellion, which was finally crushed after Martial law was declared. The Italian government blamed anarchists and the Church, specifically the Archbishop of Palermo, for the rebellion and began enacting anti-Sicilian and anti-clerical policies. A new cultural, economic and industrial growth was spurred by several families, like the Florio, the Ducrot, the Rutelli, the Sandron, the Whitaker, the Utveggio, and others. In the early twentieth century Palermo expanded outside the old city walls, mostly to the north along the new boulevards Via Roma, Via Dante, Via Notarbartolo, and Viale della Libertà. These roads would soon boast a huge number of villas in the Art Nouveau style. Many of these were designed by the famous architect Ernesto Basile. The Grand Hotel Villa Igiea, designed by Ernesto Basile for the Florio family, is a good example of Palermitan Art Nouveau. The huge Teatro Massimo was designed in the same period by Giovan Battista Filippo Basile, and built by the Rutelli & Machì building firm of the industrial and old Rutelli Italian family in Palermo, and was opened in 1897.
Which families help to start cultural, industrial, and economic growth in Palermo?
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The answer: Florio, the Ducrot, the Rutelli, the Sandron, the Whitaker, the Utveggio


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In abstract algebra, more general structures are defined by relaxing some of the axioms defining a group. For example, if the requirement that every element has an inverse is eliminated, the resulting algebraic structure is called a monoid. The natural numbers N (including 0) under addition form a monoid, as do the nonzero integers under multiplication (Z ∖ {0}, ·), see above. There is a general method to formally add inverses to elements to any (abelian) monoid, much the same way as (Q ∖ {0}, ·) is derived from (Z ∖ {0}, ·), known as the Grothendieck group. Groupoids are similar to groups except that the composition a • b need not be defined for all a and b. They arise in the study of more complicated forms of symmetry, often in topological and analytical structures, such as the fundamental groupoid or stacks. Finally, it is possible to generalize any of these concepts by replacing the binary operation with an arbitrary n-ary one (i.e. an operation taking n arguments). With the proper generalization of the group axioms this gives rise to an n-ary group. The table gives a list of several structures generalizing groups.
What product is created if the requirement that every element has an inverse is eliminated?
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The answer:
monoid