Chemistery Essay Example | Topics and Well Written Essays - 750 words - 1

Chemistery - Essay Example Suggest a suitable (iv) Using curly arrows, draw a mechanism to account for the synthetic transformations from 4 to 3 and then to 2.reagent for this reaction. Using curly arrows, draw a mechanism for this reaction. (ii) 2-Methoxybuta-1,3-diene (9) can react with ethyl propenoate (10) under thermal conditions. Identify the major product of this reaction. Use curly arrows to indicate the bond making and breaking steps which form the product. 3.Usnic acid (12) is a dibenzofuran derivative found in several lichen species and possesses a wide range of biological functions, including antibacterial properties. Usnic acid can be readily formed from compound 11, which can be prepared from compound 13 by a sequence of reactions. (Note: compound 13 is a minor tautomer of compound 13a.) Carry out a retrosynthetic analysis of compound 13, showing that 14 and 15 are the starting reagents. Your retrosynthetic analysis should clearly indicate the disconnections, the synthons thus generated and the reagents corresponding to each

DIOPHANTUS A KEY FIGURE IN THE HISTORY OF ALGEBRA Essay

DIOPHANTUS A KEY FIGURE IN THE HISTORY OF ALGEBRA - Essay Example He was a Greek mathematician who was born, raised and lived in Alexandria in Egypt which was considered a striking center for learning and culture in the Greek world. During his time he was best known for his collection of books arithmetica which was a landmark work in the algebra history. He had a very huge influence on the development of number theory with the Diophantine equations (Book Rags, n.d). Diophantus’ book The Arithmetica was a much higher one on level compared to the others as it had (or it gave) many amazing solutions to the difficult indeterminate equations. He was very keen as he did not have any impression for zero and tried as much as he could to avoid negatives in his equations. His keenness drove him at three types of quadratic equations that include ax2 + bx = c, ax2 = bx + c and ax2 + c = bx. However despite him using the three types, today’s mathematics only one case (only one quadratic equation) is looked at. He also considered other various types of problems. He was good at solving many mathematics problems that included the pairs of simultaneous quadratic equations (Algebra.com) Diophantus made many contributions to algebra and one of contributions which will be discussed in detail is the problems of Arithmetica. There are six books of Arithmetica that present the indeterminate and determinate problems and they are treated using algebraic inequalities and algebraic equations. Diophantus moves from the simple to difficult in the degree of the unknown numbers and equations. All his works are summed in the sixth book which has a number of exercises that belong to a variety of group problems. The exercises are related to the right triangle and without taking into consideration the dimensions; the polynomials are created from the surface and from the sides and once from the angle bisector (encyclopedia.com., 2011). The first book by Diophantus contains the determinate problems that are of the second and the first degree.