Publications

Publications:

Mathematics Magazine
1. "Solution to Problem #648," 40 (Sept. 1967) 228.
2. "Averages on the Move," 58 (May 1985) 151-156. Co-authored with Ivan Niven.
3. "Summations Involving Computer-Related Functions,"62 (June 1989) 191-196. Co-authored with Jim Ridenhour.
4. "Solutions of x^n + y^n = z^(n+1) ," 62 (Dec. 1989) 342.
5. "A New Proof of the Double Butterfly Theorem," 63 (Oct. 1990) 256-257.
6. "A Menelaus-Type Theorem for the Pentagram," 66 (Apr. 1993) 121-123.
7. "Mathematical Quickie #866," 70 (June 1997) 224 & 229.
8. "Mathematical Quickie #869," 70 (Oct. 1997) 299 & 307.
9. "Problem Proposal #1574," 72 (June 1999) 236.
10. "Problem Proposal #1635," 74 (Dec. 2001) 403.
11. "Extriangles and Excevians," 74 (Dec. 2001) 384 - 388.
12. "Problem Proposal #1653," 75 (Oct. 2002) 317.

College Mathematics Journal
1. "Problem Proposal #114," 9 (Mar. 1978) 95.
2. "A Geometrical Interpretation of the Weighted Mean," 15 (Mar. 1984) 135-139.
3. "Solution to Problem #227," 15 (Mar. 1984) 165-166.
4. "Problem Proposal #325," 17 (Mar. 1986) 185.
5. "Problem Proposal #347," 18 (Mar. 1987) 160.
6. "Some Properties of Polygons Inside a Circle," 18 (Nov. 1987) 397-401.
7. "Problem Proposal #387," 19 (Nov. 1988) 448.
8. "Problem Proposal #515," 24 (Nov. 1993) 473.
9. "A Concurrency Theorem and Geometer's Sketchpad," 28 (Mar. 1997) 129-132.
10. "Area Relations of the Skewed Chessboard," 34 (May 2003) 232-236.

Mathematics Teacher
1. "A More Elegant Method of Deriving the Quadratic Formula," 68 (May 1975) 442-443.
2. "Some Novel Consequences of the Midline Theorem," 70 (Mar. 1977) 250-251.
3. "Goldilocks and the Three NumBEARS," 77 (Dec. 1984) 666 & 692.
4. "Reader Reflections: Ratios of Arithmetic Progressions," 79 (Nov. 1986) 591 & 624.
5. "Reader Reflections: Werick Theorem Revisited," 81 (Feb. 1988) 85.
6. "Reader Reflections: Some Theorems Revisited I," 81 (Nov. 1988) 697-698.
7. "Geometrical Inequalities via Bisectors," 82 (Feb. 1989) 96-99.
8. "Book Review of Ore's Number Theory and Its History," 82 (Feb. 1989) 148.
9. "Calender Problems," 83 (Jan 1990) 37-40; 83 (Feb. 1990) 121-124; 83 (Mar. 1990) 204-208; 83 (Apr. 1990) 289-293; 83 (May 1990) 373-376.
10. "Problem Posing in Geometry," 84 (Jan. 1991) 10-14.
11. "Reader Reflections: A New Proof of the Pythagorean Theorem," 88 (Feb. 1995) 168.
12. "Reader Reflections: Extra Digits," 89 (Feb. 1996) 148.
13."The Pythagorean Theorem: An Infinite Number of Proofs?,"90 (Sept. 1997) 438-441. Printing error corrected 91 (Jan. 1998) 73.
14. "Reader Reflections: Median of a Trapezoid," 92 (Sept. 1999) 522-523.
15. "Reader Reflections: Angles Formed by Chords and Secants," 93 (Mar. 2000) 237-238.
16. "Book Review of Developing Mathematical Reasoning in Grades K-12," 93 (Mar. 2000) 254-255.
17. "Reader Reflections: Meeting the Challenge," 93 (Apr. 2000) 265.
18. "Reader Reflections: A Dissection Proof," 94 (Feb. 2001) 105.
19. "Reader Reflections: Pseudo-Inverse Functions," 95 (Dec. 2001) 723.
20. "Reader Reflections: Outside the Box," 95 (Jan. 2002) 52.
21. "Book Review of Laczkovich's Conjecture and Proof," 95 (Oct. 2002) 553.
22. "Book Reviews of A Little Book of Coincidence, Platonic and Archimedean Solids, and Stonehenge," 96 (Feb. 2003) 154.

Mathematical Gazette
1. "A Simple Generalization of Ceva's Theorem," 73 (June 1989) 126-127.
2. "The Golden Ratio Via Ptolemy's Theorem," 74 (Oct. 1990) 279-283.
3. "Pythagoras Inside Out," 80 (Nov. 1996) 544-545.
4. "Tangential Properties of Pentagrams," 81 (July 1997) 281-282.
5. "Circumradius of a Cyclic Quadrilateral," 84 (Mar. 2000) 69-70.
6. "A Neglected Pythagorean-Like Formula," 84 (Mar. 2000) 71-73.
7. "Weighted Mean in a Trapezium," 84 (Mar. 2000) 102-103.
8. "Perpendiculars and Inscribed Polygons," 84 (Nov. 2000) 502-504.
9. "A Ceva-Type Theorem for the Cyclic Quadrilateral," (accepted 2003).

Missouri Journal of Mathematical Sciences
1. "Problem Proposal #71," 6 (Spring 1994) 98; "Solution," 7 (Spring 1995) 91-93. Co-authored with Jim Ridenhour and Ronnie Gupton.
2. "Problem Proposal #80," 7 (Winter 1995) 40; "Solution," 8 (Winter 1996) 43-45.
3. "Solution to Problem #67," 7 (Spring 1995) 43.
4. "Concurrency Theorems for Pentagrams," 8 (Fall 1996) 125-133.
5. "Problem Proposal #120," 10 (Spring 1998) 118; Solution: 11 (Fall 1999) 208.
6. "Problem Proposal #124," 10 (Fall 1998) 177; Printing error corrected 11 (Winter 1999) 45-46. Solutions I & II: 12 (Winter 2000) 62-66.
7. "Problem Proposal #134, 13 (Fall 2001) 206.

Miscellaneous Mathematical Articles
1. "Mittlinjesaten," Elementa, 62 (May 1979) 89-90.
2. "A More Proficient Method of Factoring," International Journal of Mathematical Education in Science and Technology, 17 (Sept.-Oct. 1986) 636-639.
3. "On Napoleon's Theorem," Ellipse, 1 (Summer 1993) 8.
4. “Algebraic Diet Plan,” Centroid, 22 (Spring 1995) 30.
5. "Gaskets Galore," Mathematics and Computer Education, 29 (Fall 1995) 262-268. Co-authored with Jim Ridenhour and Thomas Hamel.

Theses, Books, and Chapters
1. Some Mean Value Theorems of Differential Calculus, M.A. Thesis, University of Tennessee, Feb. 1971, 72 pages.
2. An Experimental Study of Teaching A Mathematical Concept via Positive and Negative Instances, Ed.D. Dissertation, University of Tennessee, Aug. 1973, 80 pages.
3. "Probability in High School Geometry," Learning and Teaching Geometry, K-12, 1987, NCTM Yearbook, 1987, pages 175-183. Mary Lindquist (ed.). Co-authored with Ernie Woodward.
4. Classical and Modern Geometry, APSU, 1992. 200 pages.
5. "Chapter 27: Problem Posing in Geometry," Problem Posing: Reflections and Applications, Brown & Walters (ed.), Lawrence Erlbaum Associates, 1993, pages 281-288.
6. "A Neglected Pythagorean-Like Formula," The Changing Shape of Geometry: Celebrating a Century of Geometry and Geometry Teaching, Chris Pritchard (ed.), Cambridge University Press, 2003, pages 228-231.
7. "Pythagoras Inside Out," The Changing Shape of Geometry: Celebrating a Century of Geometry and Geometry Teaching, Chris Pritchard (ed.), Cambridge University Press, 2003, pages 544-545.

Non-Mathematical Publications
1. "The Ledger of J.W. Cramer, M.D., Jackson, MO,” St. Louis Genealogical Society Quarterly, 11 (Winter 1978) 107-114 & 12 (Spring 1979) 5-12.
2. “A Genealogical History of Luther Chapel, Perry County, MO,” St. Louis Genealogical Society Quarterly, Vol. X (Sept. 1977) 73-77.
3. "Some Records of Luther Chapel Evangelical Lutheran Church of Perry County, MO," St. Louis Genealogical Society Quarterly, XII (no. 3 ca. 1980) 94 - 97.
4. The Hoffman-Schemel Families, Lineage Press, St. Louis, MO, 1982, 334 pages.
5. Genealogist and Historian's Guide to Perry County, Missouri, Lineage Press, 1985, 42 pages.
6. “The Naming of Friedenberg,” Perry County Heritage, 1990s.
7. The Hoehn Families: Runtzenheim to Friedenberg, Lineage Press, 2003, 542 pages.