A survey of the spherical space form problem - download pdf or read online

By J. F. Davis

ISBN-10: 3718602504

ISBN-13: 9783718602506

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This can be the 3rd released quantity of the court cases of the Israel Seminar on Geometric facets of useful research. the big majority of the papers during this quantity are unique study papers. there has been final yr a robust emphasis on classical finite-dimensional convexity idea and its reference to Banach house thought.

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IV, THE STRAIGHT LINE 26] Find the equation of the 3. and § — 37 whose intercepts are 3 line 1. 4. Does the line joining the two points (6, 0) and through the point (3, 2) ? the point (— 4, 5) ? 5. >) and (x^, y^ ? The 6. 4) pass (x^, y^) lies and (7, - 3) is divided Find the equation of the line joining line joining the points (6, 2) in the ratio of 2 to 5. the point (0, — 5) (—5, to the point of division. The coordinates of the vertices of a triangle are {2, 1), and (-4, - 1). Find the equation of the medians, and show that the coordinates of the point of intersection of 7.

A 6. equation of A 7. A 8. (0, 0) sum (5, of the squares of its — 5) is always equal to its locus. point moves so as to be always three times as far from the point two axes and — (1, 2) as from the point (—3, sum point moves so that the is 4). Find the its locus. equal to point moves so that always one-half its of its distances from the Find the equation of 10. its its locus. distance from the X-axis distance from the origin. is Find the equation of its locus. A 9. (—4, point moves so always equal to the equation of its locus.

If the equations of the sides of a triangle are 3x +y—7 =0, and x each of the medians. / find the length of : Ch. Ill, § 4. LOCI 21] Which 33 of the points (3, -1), (7, 2), (0, -2), are on the locus of the equation 4 x 5. of X6. / and (8, 3) 14. Find the length of the chord of intersection of the 2/' = 13 and y'~ = 3x-\-3. loci + For what values of b are the two intersections of the y = 2x -\-b and y- = 4x real and distinct ? imaginary ? loci of coincident ? 7. Write a single equation which will represent the two bisectors of the angles between the axes.

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A survey of the spherical space form problem by J. F. Davis

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