Smith, Geoff - Department of Mathematical Sciences, University of Bath

• Some Circles in a Cyclic Quadrilateral Christopher J Bradley
• Article: CJB/2011/133 Conics in a Semi-Regular Hexagon
• Article: CJB/2010/92 Three special Cyclic Quadrilaterals
• Article: CJB/2010/85 A Converse of the Pascal Line Property
• Article: CJB/2010/112 Parallels from the feet of Cevians create a Conic
• Article: CJB/2010/91 Christopher Bradley
• More on the Seven-Point Circle Christopher J Bradley
• Article: CJB/2010/98 Ex-points and their Sets of Intersecting Circles
• Groups Sheet 4 Please do not submit solutions. Study the official solutions when they are issued.
• Article: CJB/2010/122 Some lines through the Incentre I
• Article: CJB/2011/139 The Harmonic Cevian Conic
• Constructing Two Coaxal systems by Incidence and Reflection Christopher J Bradley
• Eight points on a line and seven circles through a point Christopher J Bradley
• Article: CJB/2010/87 Two connected Rectangular Hyperbolae
• Groups Sheet 1 1. Let G be a group. Suppose that x G. Consider the maps x, x
• Article: CJB/2010/93 Circles formed by an Isosceles Trapezium
• SIX POINTS ON A CIRCLE Christopher J Bradley
• The Miquel Circles for a Quadrilateral Christopher J Bradley
• Article: CJB/2011/128 The Symmetry of a Scalene Triangle
• On the Nine Intersections of Two Cevian Triangles Christopher J Bradley
• More on Circular Perspective Christopher J Bradley
• Three Triangles in Mutual Triple Perspective Christopher Bradley
• A Cascade of Conics Christopher J Bradley
• Article: CJB/115/2010 Six Circles and their Centres
• Circles concentric with the Circumcircle Christopher J Bradley
• Article: CJB/116/2010 The Geometry of the Brocard Axis and Associated Conics
• The Circle centre O and radius OH Christopher J Bradley
• Article: CJB/2011/134 When the Cevian Conic is a Circle
• Article: CJB/2011/142 Incircle Conjugation
• Groups Sheet 2 Solutions version 2 Please submit solutions to prime numbered problems by 12:15 on Monday February 28.
• Groups Sheet 3 Please submit solutions to even numbered problems by 12:15 on Monday March 7.
• Groups Sheet 3 Solutions version 1 Please submit solutions to even numbered problems by 12:15 on Monday March 7.
• Groups Sheet 4 Please do not submit solutions. Study the official solutions when they are issued.
• STUDIES IN SIMILARITY Christopher J Bradley
• Miquel circles and Cevian lines Christopher J Bradley
• A New Construction to find any Circle through a Given Point Christopher J Bradley
• Ex-points and eight intersecting circles Christopher J Bradley
• Intersecting Circles having chords the sides of a Cyclic Quadrilateral Christopher J Bradley
• Circular Perspective Christopher J Bradley
• Significant Points on Circles Centre the Circumcentre Christopher J Bradley
• The Thirteen point Circle Christopher J Bradley
• A circle concentric with the incircle Christopher J Bradley
• More cases of Circular Perspective Christopher J Bradley
• Some Circles in the Cyclic Quadrilateral configuration Christopher J Bradley
• More Circles in the Cyclic Quadrilateral Configuration Christopher J Bradley
• Triangle and its Euler line Christopher J Bradley
• Triangle and its Euler Line Christopher J Bradley
• Triangle and its Euler Line and Circles Christopher J Bradley
• A natural Enlargement and a resulting Collineation Christopher J Bradley
• Hagge Circles touching at H Christopher Bradley
• Four Triangle Conics Christopher J Bradley
• Perpendiculars to a Triangle's Sides through its Vertices Christopher J Bradley
• Additional results for the Miquel configuration Christopher J Bradley
• 7 Points on any Circle not through a Vertex Christopher J Bradley
• Centroid-centred Similar Ellipses Christopher J Bradley
• Concurrent lines in a Triangle with a Circle cutting the Sides Christopher J Bradley
• A Triangle with an Arbitrary Conic cutting its Sides Christopher J Bradley
• What happens when a Triangle is Rotated about its Orthocentre Christopher J Bradley
• More Special Cyclic Quadrilaterals Christopher J Bradley
• The Double Simson Line Conic Christopher J Bradley
• Conics in the Ex-circle Configuration Christopher J Bradley
• Article: CJB/82/2010 Cevian derived Conics
• Article: CJB/82/2010 Conics generated by Points on a Curve of degree Five
• Article: CJB/2010/84 The G Circles and the Conic they determine
• Article: CJB/2010/89 Perpendiculars in a Cyclic Quadrilateral
• Article: CJB/2010/94 Generalization of the Steiner Point
• Article: CJB/2010/100 Circles though a point in an Equilateral Triangle
• Article: CJB/2010/102 Two Triangles, their Ex-Symmedians and four Conics
• Article: CJB/2010/103 The Altitudes Create Four Circles, Four Conics and a Polar line
• Article : 2010/CJB/104 How any Six Points on a Circle create Two Conics
• Article CJB/2010/105 External Squares on the Sides of a Triangle
• Article: CJB/2010/106 On Perpendiculars at the corners of a Cyclic Quadrilateral
• Article: CJB/2010/107 Conics through three points with Centres on a Fixed Line
• Article: CJB/109/2010 Four Perspectives given a Triangle and its Circumcircle
• CJB: Article/2010/111 Perpendicular bisectors of Three Radii of a Circle
• Article: CJB/2010/114 Properties of a Particular Tucker Circle
• Article: CJB/117/2010 When the Cevians of triangle ABC meet the Circumcircle at D, E, F
• Article: CJB/2010/119 The Nine-point Conic and a Pair of Parallel Lines
• Article: CJB/2010/120 An Important Line through the Centre of a Cevian Inellipse
• Article: CJB/2010/124 Two Cevian Points Collinear with a Vertex and Thirteen Conics
• Article: CJB/2011/127 When a Circle passes through a Vertex and cuts the Opposite Side
• Article: CJB/2011/132 The Cevian Conic
• Article: CJB/2011/135 Constructing Triangles with Coincident Centroids
• Article: CJB/2011/138 Explaining some Collinearities amongst Triangle Centres
• Article: CJB /2011/140 The Centroid of Centroids
• Article: CJB/2011/141 Three Centroids created by a Cyclic Quadrilateral
• Article: CJB/2011/144 Four Nine-Point Circles
• Article: CJB/2011/150 When a Point is a Circumcentre, an Incentre and an Orthocentre
• Two Cyclic Quadrilaterals and Two Coaxal Systems Christopher J Bradley
• Article: CJB/2010/108 A Property of 3 Circles passing through a fixed Point
• MA10209 Algebra 1A Sheet 3 Hand in this work by 12:15 on Monday Nov 16
• MA10209 Algebra 1A Sheet 4 Solutions Hand in this work by 12:15 on Monday Nov 30
• MA10209 Algebra 1A Sheet 6 Do this work by Week 15
• Article: CJB/2010/123 Properties of the Intangential Triangle
• Groups Sheet 2 Please submit solutions to prime numbered problems by 12:15 on Monday February 28.
• Perpendicular Bisectors and Angle Bisectors Christopher Bradley
• On The Ten Point Wood-Desargues' Configuration Christopher J Bradley and Geoff C Smith
• A Special Tucker Circle Christopher J Bradley
• The Simson Line Porism Christopher J Bradley
• A Cyclic Quadrilateral, 29 Points and 33 Lines Christopher J Bradley
• The Altitudes and Radii of a triangle and its circumcircle Christopher J Bradley
• Six Collinear Points in a Special Cyclic Quadrilateral Christopher J Bradley
• Generalization of the Wallace-Simson line Christopher J Bradley
• Article: CJB/2011/129 The Neuberg Cubic
• The GH Disc and another case of Triple Circular Perspective Christopher J Bradley
• Article: CJB/2010/81 A Radical Centre that lies on OI
• On the Circles defining the Brocard Points Christopher J Bradley
• Harmonic ranges in a coaxal system of circles Christopher J Bradley
• Article: CJB/2011/126 Some Properties of the Ex-Circle configuration
• Article: CJB/2010/118 Two Triangles in Perspective and inscribed in a Conic
• Porisms with a circular circumconic C J Bradley and G C Smith
• Article: CJB/2010/110 Three Concurrent Pascal lines and an Auxiliary Conic
• Omega Circles Christopher J Bradley
• When one Conic produces two more Christopher J Bradley
• The Double Simson Line Circle Christopher J Bradley
• Article: CJB/2010/96 More on the Nine Point Rectangular Hyperbola
• Practice Exam Solutions 2 hours, no calculators
• Generalizations of Hagge's Theorems Christopher J Bradley
• The Direct Similarity of the Miquel Point Configuration Christopher J Bradley
• Article: CJB/2011/137 Affine Transform of the properties of the Euclidean Triangle
• MA10209 Algebra Sheet 1 Solutions version 2 Hand in this work by 12 noon on Monday Oct 19
• MA10209 Algebra 1A Sheet 5 Solutions Hand in this work by 12:15 on Monday Dec 14
• Christmas Assessment Exercise, 2005 c G.C.Smith
• Article: CJB/2011/148 A Circle through two Vertices, three Circumcentres and a Miquel
• Article: CJB/2010/101 Intersections at the vertices of the Second Brocard Triangle
• Article: CJB/2011/125 Properties of the Extangential Triangle
• MA10209 Algebra 1A Sheet 3 Hand in this work by 12:15 on Monday Nov 16
• MA10207 and MA10209 schedule Geoffrey and Geoff
• The Four Hagge circles Christopher J Bradley
• Article: CJB/2011/149 Circles with a common point in a Cyclic Quadrilateral
• When quadrangles are completely in perspective Christopher J Bradley
• Christopher J Bradley 1. Introduction
• On the mean of two Cevian points Christopher J Bradley
• Where 7 Circles meet Part 2 Christopher J Bradley
• MA10209 Algebra 1A Sheet 3 Hand in this work by 12:15 on Monday Nov 16
• MA10209 Algebra 1A Algebraic Structures
• A Mean of two Cevian Points and the Construction of Triangle Centres Christopher J Bradley
• Where Seven Circles meet Christopher J Bradley
• When I replaces K and Ge replaces H and Mi replaces O Christopher J Bradley
• Eight circles through the Orthocentre Christopher J Bradley
• Article: CJB/88/2010 A Singular Cyclic Quadrilateral
• The Cevian point Conic Christopher Bradley
• Porism created by the Circumcircle and Triangles in Perspective Christopher J Bradley
• Article: CJB/2010/99 A Triangle and its Image under a Half Turn
• Article: CJB/2010/86 The Perpendiculars to Three Segments at a Point determine a Conic
• Article: CJB/2010/113 Circles passing through the Miquel Point of the feet of Cevians
• Article: CJB/2011/146 More Conics in a Semi-Regular Hexagon
• The Symmedian point and the Polar Line C J Bradley
• SOLUBLE GROUPS WITH A FINITE REWRITING SYSTEM J.R.J. Groves & G.C. Smith
• Perpendiculars to the Cevians at the Cevian Point Christopher Bradley
• Article: CJB/2011/136 Properties of the Symmedian points in a Cyclic Quadrilateral
• Three triangles in mutual Triple Reverse Perspective Christopher J Bradley
• Article: CJB/2011/130 An Extension to the Theory of Hagge Circles
• Some Special Circles in a Triangle Christopher J Bradley
• Article: CJB/2011/143 The Nine Point Circle of the Diagonal Point Triangle
• A Cevian point and its Six Harmonics Christopher Bradley
• FINITE p-QUOTIENTS OF SOME CYCLICALLY PRESENTED GROUPS HUSEYIN AYDIN AND GEOFF C. SMITH
• Fourier Analysis in Finite Nilpotent Groups
• Wall and Vinson Revisited Huseyin Aydin Ramazan Dikici*
• Chaos, Elliptic Curves and All That Matthew Fletcher *
• Article: CJB/2010/95 A Nine Point Rectangular Hyperbola
• What happens when you reflect a Triangle in any Line Christopher J Bradley
• Incircle and Excircle Conics Christopher J Bradley
• Article: CJB/2010/121 Some Lines through the Centroid G
• MA10209 Algebra 1A Sheet 6 Do this work by Week 15
• Article: CJB/2011/131 Construction of Circles always having centre the Nine-Point Centre
• The Story of Hagge and Speckman Christopher J Bradley
• Groups Sheet 1: solutions (v2) 1. Let G be a group. Suppose that x G. Consider the maps x, x
• A Singular Miquel Configuration and the Miquel Direct Similarity Christopher J Bradley
• Article: CJB/2011/147 The Midpoint Rectangular Hyperbola again
• Article: CJB/97/2010 How the Excentres create Points on the Circumcircle
• Article: CJB/2010/90 Perpendiculars from the vertices of a Cyclic Quadrilateral
• Proving another group infinite. Geoff C. Smith
• A NOTE ON FERMAT'S LITTLE THEOREM AND INTEGER MATRICES
• ON MONOIDS WITH A SINGLE DEFINING RELATOR G. C. Smith
• Fresh Orderings of Groups G. C. Smith O. M. Tabachnikova
• MA10209 Algebra Sheet 2 Solutions Hand in this work by 12 noon on Monday Nov 2
• Four Concurrent Euler Lines Christopher J Bradley
• Article: CJB/2011/168 Properties of a pair of Diametrically Opposite Triangles
• Article: CJB/153/2011 More properties of the Incentre
• Article: CJB/2011/169 Two In-Perspective Triangles inscribed in a Conic
• Article: CJB/2011/162 When 24 Points form three 8-point Conics and 12 Concurrent Lines
• Article: CJB/2011/158 Six Point Circles and their Associated Conics
• Article/CJB/165 A description of properties of Pascal's hexagon
• Article: CJB/2011/157 The General Inellipse
• Article: CJB/2011/167 Basic Properties of a Quadrangle possessing an Incircle
• Article: CJB/2011/164 The Transversal of a Quadrilateral
• Article: CJB/2011/152 Generating Circles from the Symmedian point
• Article: CJB/2011/160 Tangents to a Conic from the vertices of a Triangle
• Article: CJB/2011/163 A Theorem on the Complete Quadrilateral
• Article: CJB/2011/166 Analytic treatment of a Romanian problem
• Article: CJB/2011/155 The Circumconic of a pair of Cevian Triangles
• Article: CJB/2011/170 The Brocard Conics
• Article: CJB/2011/151 The Orthocentre Conics
• Article: CJB/2011/154 On the Incircle and Excircles of a Cevian Triangle
• Article: CJB/2011/159 A Twelve Point Configuration and Carnot's Theorem
• Article: CJB/2011/156 Circumcentre Conics
• MA10209 Algebra 1A Sheet 8 Problems v1: GCS
• Article CJB/2011/184 Cevian Perspectivity
• Article: CJB/2011/175 When two Triangles intersect in Conics and in Circles
• Article: CJB/2011/183 Conics and Triangles in Perspective
• MA10209 Algebra 1A Sheet 3 Problems and Solutions v2: GCS
• MA10209 Algebra 1A Sheet 6 Problems and Solutions v3: GCS
• Article: CJB/180/2011 Circles through the Brocard points and the Circumcentre
• MA10209 Algebra 1A Sheet 9 Problems v1: GCS
• Boolean Algebra Information Sheet c G.C.Smith 2010
• MA10209 Algebra 1A Sheet 4 Problems v0: GCS
• Article: CJB/2011/185 The Four Conic Theorem
• MA10209 Algebra 1A Sheet 7 Problems v2: GCS
• Article: CJB/2011/178 More Circles centred on the Brocard Axis
• MA10209 Algebra 1A Counting Partitions: GCS
• MA10209 Algebra 1A Sheet 10 Problems v0: GCS
• MA10209 Algebra 1A Sheet 2 Problems v1: GCS
• MA10209 Algebra 1A Sheet 7 Problems and Solutions v3: GCS
• Article: CJB/2011/187 A Perspective in a pair of Cyclic Quadrilaterals
• Article: CJB/2011/172 The Inner Circle of a Cyclic Quadrilateral
• MA10209 Algebra 1A Sheet 5 Problems v0: GCS
• Article: CJB/179/2011 The Second Brocard Triangle
• Article 174/cjb/2011/174 A Cevian Circle leads to Perspective Triangles
• MA10209 Algebra 1A Sheet 9 Problems and Solutions v1: GCS
• Article: CJB/2011/182 Problems requiring Proof
• MA10209 Algebra 1A Sheet 8 Problems and Solutions v1: GCS
• Article: CJB/2011/171 A Conic through the feet of two Cevians may lead to a second Conic
• MA10209 Algebra 1A Sheet 5 Problems and Solutions v2: GCS
• MA10209 Algebra 1A Sheet 1 v2: GCS
• Article: CJB/2011/181 Circles through the Brocard points and the Symmedian Point
• Article: CJB/2011/189 The Midpoint Conic
• Article/CJB/2011/176 Orthologic Triangles
• Article: CJB/2011/186 6 Points and 4 perspectives
• Article: CJB/2011/188 Are three Triangles ever in Mutual Perspective
• Article/CJB/2011/177 Special Pascal Lines
• MA10209 Algebra 1A Sheet 3 Problems v1: GCS
• MA10209 Algebra 1A Sheet 4 Problems and Solutions v1: GCS
• Article: CJB/2011/173 The Auxiliary Circles of a Cyclic Quadrilateral
• MA10209 Algebra 1A Sheet 10 Problems and Solutions v0: GCS
• MA10209 Algebra 1A Solutions to vacation Problems v0: GCS
• MA10209 Algebra 1A Vacation Problems v0: GCS