The advanced geometry of plane, curves and their applications/
Zwikker, C.
The advanced geometry of plane, curves and their applications/ C. Zwikker - New York: Dover, 2005. - xii, 299 p. : ill. ; 23 cm. - Dover phoenix editions. .
PREFACE;
CHAPTER I - THE COMPLEX PLANE; 1. Introduction; 2. First examples; 3. Intersection of two curves. Complex x- and y-values; 4. The elements at infinity; 5. Complex values of u, deficient curves;
CHAPTER II - THE GEOMETRICAL INTERPRETATION OF ANALYTIC OPERATIONS APPLIED TO COMPLEX NUMBERS; 1. Addition, subtraction, multitiplication; 2. Decomposition of complex numbers; 3. Quotients; 4. Conformal transforms, inversion.; 5. Non-conformal transforms, collineation; 6. The first derivative, tangents; 7. The second derivative, curvature.
CHAPTER III - THE STRAIGHT LINE1. Collinearity of three points, concurrency of three straight lines; 2. The theorems of Ceva, Menelaos and Desargues; 3. Line coordinates; 4. Polar transformation, dual conceptions; 5. Projective point assemblages and ray pencils; 6. Projective geometry; 7. Involution;
CHAPTER IV - THE TRIANGLE; 1. Centre of gravity, orthocentre, circumcentre; 2. Euler's axis, nine points circle; 3. Base points of perpendiculars, Wallace's theorem; 4. Steiner's cycloid;
CHAPTER V - THE CIRCLE; 1. Properties of constant angle and of constant power; 2. General circle formula. 3. Circuit impedance and admittance. 4. The circle transformation; 5. Projective properties;
CHAPTER VI - ALGEBRAIC CURVES; 1. Unicursal curves of the n-th order; 2. Synthetic construction of conics, cubics and quartics; 3. Pole and polar; 4. Pascal's and Brianchon's theorems; 5. Cubics, Newton's classification; 6. Cubics, projective porperties;
CHAPTER VII - THE ELLIPSE; 1. Introduction; 2. Conjugate diameters; 3. The foci; 4. Kepler orbits; 5. Conic sections; 6. The reflection law; 7. The perimeter of the ellipse, radius of curvature;
CHAPTER VIII - HYPERBOLA; 1. Introduction. 2. Medians, conjugate directions3. Foci; 4. Ordhogonal Hyperbola; 5. Cartesian ovals;
CHAPTER IX - THE PARABOLA; 1. Introduction; 2. Right angles in the parabola; 3. Medians, pole and polar; 4. Concluding remarks on conics;
CHAPTER X - INVOLUTES, EVOLUTES, ANTICAUSTICS; 1. Involute and evolute; 2. Norwich spiral; 3. Catenary and tractrix; 4. Tractrices in general; 5. The evolute of the parabola; 6. Anticaustics;
CHAPTER XI - PEDALS AND OTHER DERIVED CURVES; 1. Pedal and contrapedal; 2. The pedal inversion theorem; 3. Limaçon, conchoid; 4. Pedals derived from the parabola.
CHAPTER XV - KINKED CURVES.
0486442764
Curves
Geometry, Plane
516.22 / ZWI/A
The advanced geometry of plane, curves and their applications/ C. Zwikker - New York: Dover, 2005. - xii, 299 p. : ill. ; 23 cm. - Dover phoenix editions. .
PREFACE;
CHAPTER I - THE COMPLEX PLANE; 1. Introduction; 2. First examples; 3. Intersection of two curves. Complex x- and y-values; 4. The elements at infinity; 5. Complex values of u, deficient curves;
CHAPTER II - THE GEOMETRICAL INTERPRETATION OF ANALYTIC OPERATIONS APPLIED TO COMPLEX NUMBERS; 1. Addition, subtraction, multitiplication; 2. Decomposition of complex numbers; 3. Quotients; 4. Conformal transforms, inversion.; 5. Non-conformal transforms, collineation; 6. The first derivative, tangents; 7. The second derivative, curvature.
CHAPTER III - THE STRAIGHT LINE1. Collinearity of three points, concurrency of three straight lines; 2. The theorems of Ceva, Menelaos and Desargues; 3. Line coordinates; 4. Polar transformation, dual conceptions; 5. Projective point assemblages and ray pencils; 6. Projective geometry; 7. Involution;
CHAPTER IV - THE TRIANGLE; 1. Centre of gravity, orthocentre, circumcentre; 2. Euler's axis, nine points circle; 3. Base points of perpendiculars, Wallace's theorem; 4. Steiner's cycloid;
CHAPTER V - THE CIRCLE; 1. Properties of constant angle and of constant power; 2. General circle formula. 3. Circuit impedance and admittance. 4. The circle transformation; 5. Projective properties;
CHAPTER VI - ALGEBRAIC CURVES; 1. Unicursal curves of the n-th order; 2. Synthetic construction of conics, cubics and quartics; 3. Pole and polar; 4. Pascal's and Brianchon's theorems; 5. Cubics, Newton's classification; 6. Cubics, projective porperties;
CHAPTER VII - THE ELLIPSE; 1. Introduction; 2. Conjugate diameters; 3. The foci; 4. Kepler orbits; 5. Conic sections; 6. The reflection law; 7. The perimeter of the ellipse, radius of curvature;
CHAPTER VIII - HYPERBOLA; 1. Introduction. 2. Medians, conjugate directions3. Foci; 4. Ordhogonal Hyperbola; 5. Cartesian ovals;
CHAPTER IX - THE PARABOLA; 1. Introduction; 2. Right angles in the parabola; 3. Medians, pole and polar; 4. Concluding remarks on conics;
CHAPTER X - INVOLUTES, EVOLUTES, ANTICAUSTICS; 1. Involute and evolute; 2. Norwich spiral; 3. Catenary and tractrix; 4. Tractrices in general; 5. The evolute of the parabola; 6. Anticaustics;
CHAPTER XI - PEDALS AND OTHER DERIVED CURVES; 1. Pedal and contrapedal; 2. The pedal inversion theorem; 3. Limaçon, conchoid; 4. Pedals derived from the parabola.
CHAPTER XV - KINKED CURVES.
0486442764
Curves
Geometry, Plane
516.22 / ZWI/A