0.3 		Synthetic geometry

Kepler's explanation of the Timaeus associations, Howard Eves, 1:2, 1970, 31, C, 2.2
Shapes of the Future, Victor Klee, 2:2, 1971, 14-27, 3.1
Plaited Platonic Puzzles, Jean J. Pedersen, 4:2, 1973, 23-37
Partitions of the Plane, Nathan Hoffman, 5:2, 1974, 71-73, C, 3.1
Some Insight into the Convex Quadrilateral, Benjamin Greenberg, 5:3, 1974, 14-17
A Finite FieldÑA Finite Geometry and Triangles, Marc Swadener, 5:3, 1974, 22-26, 9.4
Polygons, Both Perfect and Regular, Richard L. Francis, 6:2, 1975, 20-21


Some Consequences of a Property of the Centroid of a Triangle, Norman Schaumberger, 8:3, 1977, 142-144
Guessing and Proving, George Polya, 9:1, 1978, 21-27
The Discovery of a Generalization: An Example in Problem Solving, Hugh Ouellette and Gordon Bennett, 10:2, 1979, 100-106, 0.2
Geometry is Alive and Well: The Coxeter Symposium in Toronto, Jean J. Pedersen, 11:1, 1980, 19-25, 1.2
Circles and Spheres, G. D. Chakerian, 11:1, 1980, 26-41
On Sets of Points in the Plane and A Property of the Binomial Coefficients, Ross Honsberger, 11:2, 1980, 116-119, 9.3
Inscribed Figures of Maximum Area: A Geometric Approach for a Geometric Problem, Peter Renz, 11:2, 1980, 147-149
The Pentagram and the Discovery of an Irrational Number, James R. Choike, 11:5, 1980, 312-316, 2.2
Euclid's 'Elements' -excerpts from a 1660 edition, 12:2, 1981, 117, 5.3.2, 5.3.3
From an Inequality to Inversion, Man-Keung Siu, 12:2, 1981, 149-151, C
A Space-Filling Torus, Dan Wheeler and David Sklar, 12:4, 1981, 246-248
An Equal Ratio Property for Convex Polygons, K. R. S. Sastry, 13:4, 1982, 270, C
The Euler Line: A Vector Approach, Norman Schaumberger, 13:5, 1982, 329-331, C
Commadino's Theorem, Norman Schaumberger, 13:5, 1982, 331, C
The Butterfly Problem and Other Delicacies from the Noble Art of Euclidean GeometryÑPart I, Ross Honsberger, 14:1, 1983, 2-8, 0.4
The Steiner-Lehmus Theorem as a Challenge problem, Ken Seydel and Carl Newman, 14:1, 1983, 72-75, 0.4, 0.6
Some Unusual Locus Problems, Shephen B. Maurer, 14:2, 1983, 146-153
The Butterfly Problem and Other Delicacies from the Noble Art of Euclidean GeometryÑPart 2, Ross Honsberger, 14:2, 1983, 154-158, 0.4
How to Make a Bank Shot, Richard C. Bollinger, 14:2, 1983, 169-170, C
How Big is a Point?, Richard J. Trudeau, 14:4, 1983, 295-300
The Construction of Integral Cevians, Charles G. Moore, 14:4, 1983, 301-308
A Tiling of the Plane with Triangles, Paul T. Mielke, 14:5, 1983, 377-381, 9.2, 9.3
On the Radii of the Inscribed and Escribed Circles of Right TrianglesÑA Second Look, Calvin T. Long, 14:5, 1983, 382-389
Ellipses from a Circular and Spherical Point of View, Alden R. Partridge, 14:5, 1983, 436-438, 0.5
Behold! The Arithmetic-Geometric Mean Inequality, Roland H. Eddy, 16:3, 1985, 208, C, 0.2
The International Mathematical Olympiad Training Session, Cecil Rousseau and Gregg Patruno, 16:5, 1985, 362-365, 2.2, 9.3
A Babylonian Geometrical Algebra, James K. Bidwell, 17:1, 1986, 22-31, 0.2
Three Ways to Maximize the Area of an Inscribed Quadrilateral, Leroy F. Meyers, 17:3, 1986, 238-239, 5.5
Behold! The Vertex Angles of a Star Sum to 180 degrees, Fouad Nakhli, 17:4, 1986, 338, C
Geometry of the Rational Plane, Larry Cannon, 17:5, 1986, 392-402
The Geometric Supposer: An Intellectual Prosthesis for Making Conjectures, Judah L. Schwartz and Michal Yerushalmy, 18:1, 1987, 58-65, 0.10
The Generalized Polygonal Cycloid, Duane W. DeTemple, 19:5, 1988, 417-419, C
Equality in Overlapping Gravitational Fields, Howard K. Justice, 20:1, 1989, 27-31
Pythagorean Theorem: aa' + bb' = cc', Enzo R. Gentile, 20:1, 1989, 58, C
Hippocrates and Archytas Double the Cube: A Heuristic Interpretation, Barnabas B. Hughes, 20:1, 1989, 42-48, 2.1
FFF #2. The Steiner-Lehmus Theorem, Ed Barbeau, 20:1, 1989, 50, F (also 20:2, 1989, 133 and 21:3, 1990, 218)
Surface Area of a Cone, Herb Holden, 20:5, 1989, 432, C
FFF #23. A Luney Way to Square the Circle, Ed Barbeau, 21:4, 1990, 302-303, F (also 22:1, 1991, 41 and 22:5, 1991, 405)
Trisection of an Angle in an Infinite Number of Steps, Eric Kincanon, 21:5, 1990, 393, C
FFF #27. Trisecting an Angle with Ruler and Compasses, Ed Barbeau, 21:5, 1990, 394-395, F (also 22:1, 1991, 41 and 23:2, 1992, 143)
Two Surprising Theorems on Cavalieri Congruence, Howard Eves, 22:2, 1991, 118-124, 2.2
A Theorem about Right Triangles, Roland H. Eddy, 22:5, 1991, 420, C
Misconceptions about the Golden Ratio, George Markowsky, 23:1, 1992, 2-19, 2.1, 2.2
Geometry: A Gateway to Understanding, Peter Hilton and Jean Pedersen, 24:4, 1993, 298-317, 9.3
A "Very Pleasant Theorem", Roger Herz-Fischler, 24:4, 1993, 318-324, 2.2
The Geometer's Sketchpad and Cabri-Geometre (software review), Dennis DeTurck, 24:4, 1993, 370-376, 0.4, 0.10
Two Trisectrices for the Price of One Rolling Coin, Jack Eidswick, 24:5, 1993, 422-430, 0.4, 9.7
Tangents to Conics, Eccentrically, Frederick Gass, 25:1, 1994, 43-45, C, 0.5
Kepler Orbits More Geometrico, Andrew Lenard, 25:2, 1994, 90-98, 5.5
A Three-Circle Theorem, R. S. Hu, 25:3, 1994, 211, C
Nothing New Under the Sun (The "Three-Circle Theorem"), H. Guggenheimer, 26:1, 1995, 10
FFF. The Spirit Is Willing But the Ham Is Rotten, John Kinloch and Rick Norwood, 26:1, 1995, 37, F
Functions of a Curve: Leibniz's Original Notion of Functions and Its Meaning for the Parabola, David Dennis and Jere Confrey, 26:2, 1995, 124-131, 0.5, 2.2
Angle Trisection by Fixed Point Iteration, L. F. Martins and I. W. Rodrigues, 26:3, 1995, 205-208, 9.6
FFF #89. A Case of Irregularity, Herb Bailey, 26:3, 1995, 221-222, F ( see also 27:4, 1996, 284)
Inductive Tiling of the Plane by Penrose Aperiodic Rhombi (by picture), Dean Clark and E. R. Suryanarayan, 26:4, 1995, 266-267, C
The 9-Point Circle Is in Fact a 12-Point Circle (by picture), Jingcheng Tong and Sidney H. Kung, 26:5, 1995, 371, C
Volume of a Frustrum of a Square Pyramid (Proof Without Words), S. H. Kung, 27:1, 1996, 32, C
Geometry Class (Peom), JoAnne Growney, 27:2, 1996, 143, C
The Moise Plane, James R. Boone, 27:3, 1996, 182-185, 9.7
Behold: The Pythagorean Theorem, Frank Burk, 27:5, 1996, 407, C
A Concurrency Theorem and Geometer's Sketchpad, Larry Hoehn, 28:2, 1997, 129-132, C
Tiling with Squares and Parallelograms (proof by picture), Alfinio Flores, 28:3, 1997, 171, C
Putting the Pieces Together: Understanding Robinson's Nonperiodic Tilings, Aimee Johnson and Kathleen Madden, 28:3, 1997, 172-181, 3.3
FFF.  The Pup Tent Problem, Ed Barbeau, 29:3, 1998, 220-221, F
A Law of Sines (proof without words), Sidney H. Kung, 29:3, 1998, 221, C
Prelude to Musical Geometry, Brian J. McCartin, 29:5, 1998, 354-370, 9.4, 9.7
FFF #139.  A Counterexample to MorleyÕs Theorem, William Watkins, 30:2, 1999, 129, F
A Far-reaching Formula, Kil S. Lee, 30:2, 1999, 138-140, C
A Simple Geometric Solution to De lÕHospitalÕs Pulley Problem, Raymond Boute, 30:4, 1999, 311-314, C, 0.6
FFF #152.  A geometry problem, Ho Juan Beng, 30:5, 1999, 383-384, F
The Pop-up Cuboctahedron, Hans Walser, 31:2, 2000, 89-92
On Lunda-Designs and the Construction of Associated Magic Squares of Order 4p, Paulus Gerdes, 31:3, 2000, 182-188, 9.2
Sum of Perpendicular Distances (Proof Without Words), Raymond Spaulding, 31:3, 2000, 244, C
The Pascal Pyramid, Hans Walser, 31:5, 2000, 383-392, 3.2
FFF #168. How to approximate a sphere, Robert Foote, 32:1, 2001, 48, F
BarrowÕs Fundamental Theorem, Jack Wagner, 32:1, 2001, 58-59, C, 5.2.1
Slippery Centroids, John M. Alongi and Steve Kennedy, 32:3, 2001, 197-199, F
HeronÕs Formula via Proofs Without Words, Roger B. Nelsen, 32:4, 2001, 290-292, C, 0.6
Upside-down Pythagorean Theorem (Mathematics Without Words), Vincent Ferlini, 33:2, 2002, 170, C
The ÒOriginÓ of Geometry, Reuben Hersh, 33:3, 2002, 207-211, 2.1, 9.2
Forming a Circle (Mathematics Without Words), James Tanton, 34:1, 2003, 14, C
A Pythagorean-like Theorem (Mathematics Without Words), Manual Moran Cabre, 34:2, 2003, 172, C
Area Relations on the Skewed Chessboard, Larry Hoehn, 34:3, 2003, 232-236, C
Lost Horizon, Richard Kubelka, 34:3, 2003, 238, C
Constructing a Poincare Line with Straightedge and Compass, David Hecker, 34:5, 2003, 362-366, 9.7
Mathematics Without Words: A Property of Secants, Norman Schaumberger, 34:5, 2003, 411, C
Another Pythagorean-like Theorem (Proof Without Words), Roger B. Nelsen, 35:3, 2004, 215, C
When Is EulerÕs Line Parallel to a Side of a Triangle?, Wladimir G. Boskoff and Bogdan D. Suceava, 35:4, 2004, 292-296, 9.7
The Golden Ratio-A Contrary Viewpoint, Clement Falbo, 36:2, 2005, 123-134, 6.3
A Non-Visual Counterexample in Elementary Geometry, Marita Barabash, 26:5, 2005, 397-400, C
FFF #246. There are no isosceles triangles, Ed Barbeau, 37:1, 2006, 41, F
Conviction With an Angle is Upheld by Court of Appeals By Michael Cooper, Jerry Porter, 37:5, 2006, 343, C
The Converse of VivianiÕs Theorem, Zhibo Chen and Tian Liang, 37:5, 2006, 390-391, C
A New Method of Trisection, David Alan Brooks, 38:2, 2007, 78-81
Rectangles, Parallelograms, or Trapezoids, Richard Syverson, 38:2, 2007, 81, 105, C (see also 38:4, 2007, 259)
An Iterative Angle Trisection, Donald L. Muench, 38:2, 2007, 82-84
A New and Improved Method for Finding the Center of Gravity of a Quadrilateral, Behzad Khorshidi, 38:3, 2007, 225-226, C
Christiaan Huygens and the Problem of the Hanging Chain, John Bukowski, 39:1, 2008, 2-11, 2.2, 5.3.3
The Right Right Triangle on the Sphere, William Dickinson and Mohammad Salmassi, 39:1, 2008, 24-33, 9.7
Universal Stoppers Are Rupert, Richard P. Jerrard and John E. Wetzel, 39:2, 2008, 90-94, 9.7
Proof Without Words: CarnotÕs Theorem for Acute Triangles, Claudi Alsina and Roger B. Nelsen, 39:2, 2008, 111, C, 9.7
The Perimeter of a Polyomino and the Surface Area of a Polycube, Wiley Williams and Charles Thompson, 39:3, 2008, 233-237, C, 9.7
Designing a Table Both Swinging and Stable, Greg N. Frederickson, 39:4, 2008, 258-266, 9.7