Download Beautiful Geometry by Eli Maor, Eugen Jost PDF

By Eli Maor, Eugen Jost

If you've ever proposal that arithmetic and artwork don't combine, this lovely visible background of geometry will swap your brain. As a lot a piece of paintings as a booklet approximately arithmetic, Beautiful Geometry offers greater than sixty beautiful colour plates illustrating quite a lot of geometric styles and theorems, followed by way of short bills of the interesting background and other people in the back of every one. With art by means of Swiss artist Eugen Jost and textual content via acclaimed math historian Eli Maor, this designated social gathering of geometry covers a variety of topics, from straightedge-and-compass structures to interesting configurations regarding infinity. the result's a pleasant and informative illustrated journey in the course of the 2,500-year-old heritage of 1 of crucial and gorgeous branches of arithmetic.

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The equation of a circle is x 2 + y 2 − 4 x + 2 y = 15 (i) Find the coordinates of the centre C of the circle, and the radius of the circle. (ii) Show that the point P (4, -5) lies on the circle. (iii) Find the equation of the tangent to the circle at the point P. [3] [1] [4] 7. The coordinates of four points are P (-2, -1), Q (6, 3), R (9, 2) and S (1, -2). [4] (i) Calculate the gradients of the lines PQ, QR, RS and SP. [1] (ii) What name is given to the quadrilateral PQRS? [2] (iii) Calculate the length SR.

Iv) Show that the equation of SR is 2y = x – 5 and find the equation of the line L through Q perpendicular to SR. [5] [3] (v) Calculate the coordinates of the point T where the line L meets SR. [3] (vi) Calculate the area of the quadrilateral PQRS. 8. AB is the diameter of a circle. A is (1, 3) and B is (7, -1). [2] (i) Find the coordinates of the centre C of the circle. [2] (ii) Find the radius of the circle. [2] (iii) Find the equation of the circle. (iv) The line y + 5x = 8 cuts the circle at A and again at a second point D.

Calculate the coordinates of D. [4] [3] (v) Prove that the line AB is perpendicular to the line CD.

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