Math 330

  • Final HW due 12/1: 9.16 (just the first sentence), 10.32, 10.39, 11.4, 12.10, 12.30, 13.1; and the following
    • A. You would like to solve \(x^3 + x = 10\) using Khayyam's method. Give the equations for, and graph, the relevant parabola and circle.
    • B. Find positive rationals \(x,y,z\) so that \(x^2 = y^2 - 6\), \(z^2 = y^2 + 6\).
  • No HW due 11/17
  • HW due 11/3: 8: 1, 22, 23 (use that (9, 82) is a solution to find another), and
    • A. Find the cube root of 74618461 using Aryabhata's algorithm.
    • B. The quadrilateral ABCD can be inscribed in a circle, and AB=25, BC=15, CD=7, AD = 15. Find the area of the quadrilateral.
    • C. Now do the cyclic quadrilateral with AB = 3, BC = 4, CD = 4, AD = 3, but do it both using Brahmagupta's formula, and by drawing AC and computing areas. Make sure to justify your reasoning!
  • No HW due 10/27. Relax!
  • HW due 10/20: §7: 17, 18, 25, 26
  • HW due 10/13: §5: 22, 24; §6: 8, 9; and the following:
    • A. Consider a triangle ABC with side lengths AB = 7, BC = 9, AC = 14. Compute exactly the length of the perpendicular from B to side AC.
    • B. Write 4 as a sum of two (positive rational) squares in 3 different ways. Graph the corresponding pictures (that is, the circle and lines).
  • HW due 10/6: §4: 11 (you may assume the chord is perpendicular to the axis of symmetry), 19, 20; and the following:
    • A. Suppose the point \(A = (a,b)\) is on the circle of radius 1 centered at the origin, and \(a > 0, b \ne 0\). What are the coordinates of the point \(B\) on the \(x\)-axis so that \(AB\) is tangent to the circle? Use Apollonius's work.
  • No HW due 9/29. For practice: §4: 1, 2, 3, 5, 6
  • HW due 9/22: §2: 13, 21; §3: 1 (use SAS), 2 (you can use midpoints), 3
  • HW due 9/15: §1: 10, 17, 25; §2: 8 (you can use a geometric proof, just explain your picture), 9, 12
  • HW due 9/8: §1: 1, 2, 4, 5, 9, 18, 24 (16 has been deleted)