27.4.1 Appendix: Solution of Pell’s equationĢ8 Polygonal triples 28.1 Double ruling of S. 26.5 Apollonius circle: the circular hull of the excirclesĢ7 Figurate numbers 27.1 Triangular numbers. 26.4 The radical circle of the excircles. 26.3 The circumcircle of the excentral triangle. Ģ5 Routh and Ceva theorems 25.1 Routh theorem: an example. 24.3.1 Appendix: Two enumerations of the rational numbers in (0,1). 24.2 Charles Twigg on the first 10 perfect numbers. 23.3 Consecutive composite values of x2 + x + 41. 23.2 Strings of consecutive composite values of n 2 + 1. Ģ3 Strings of composites 23.1 Strings of consecutive composite numbers. 22.3 The prime number spiral beginning with 41. ![]() 22.2 The prime number spiral beginning with 17. Ģ2 Strings of prime numbers 22.1 The prime number spiral. 21.3 F¨urstenberg’s topological proof made easy. Ģ1 Infinitude of prime numbers 21.1 Proofs by construction of sequence of relatively prime numbers. 20.2.3 Woo’s three constructions 20.3 More Archimedean circles. 20.2 Incircle of the shoemaker’s knife 20.2.1 Archimedes’ construction 20.2.2 Bankoff’s constructions. 523Ģ0 The shoemaker’s knife 20.1 Archimedes’ twin circles. ġ8 Repunits 517 18.1 k-right-transposable integers. 17.1.1 The Sprague-Grundy sequence 17.1.2 Subtraction of square numbers 17.1.3 Subtraction of square numbers 17.2 The nim sum of natural numbers. ġ6 3-4-5 triangles in the square 17 Combinatorial games 17.1 Subtraction games. 15.3 The digital roots of the powers of 2 15.4 Digital root sequences. 14.4 Sorted numbers with sorted squaresġ5 Digital sum and digital root 15.1 Digital sum sequences. ġ4 Numbers with many repeating digits 14.1 A quick multiplication. 337 13 Digit problems 13.1 When can you cancel illegitimately and yet get the correct answer?. 11.5 Ahlburg’s parsimonious construction of the regular pentagon. 11.3 Hofstetter’s 5-step division of a segment in the golden section. 11.2 Hofstetter’s compass-only construction of the golden section. 10.5 What is the most non-isosceles triangle?ġ1 Constructions with the golden section 11.1 Construction of golden rectangle. 304 10 The golden section 10.1 The golden section ϕ. 303 9.3 Heron triangles with consecutive sides. ĩ The area of a triangle 301 9.1 Heron’s formula for the area of a triangle. 8.2 The circumcircle and the circumcircle 8.3 The incenter and the incircle. 228 8 The classical triangle centers 8.1 The centroid. 214ħ The tangrams 225 7.1 The Chinese tangram. 213 Dissecting a rectangle into Pythagorean triangles. 212 Points at integer distances from the sides of a primitive Pythagorean triangle. Lewis Carroll’s conjecture on triples of equiareal Pythagorean triangles. 210 6.2 Primitive Pythagorean triangles with square perimeters 211 5.4 gcd of generalized Fibonacci and Lucas numbersĦ Pythagorean triples 209 6.1 Primitive Pythagorean triples. 5.3 Cassini formula for Fibonacci numbers. 5.2 Nonnegative integer combinations of a and b. ĥ Greatest common divisor 5.1 gcd(a, b) as an integer combination of a and b. 119 4 Basic geometric constructions 4.1 Geometric mean. 118 3.2 Construction of equilateral triangle inscribed in a rectangle. ![]() 111 3 Equilateral triangle in a rectangle 117 3.1 Equilateral triangle inscribed in a rectangle. ![]() ![]() 104 2 Lattice points 109 2.1 Counting interior points of a lattice triangle. Recreational Mathematics Paul Yiu Department of Mathematics Florida Atlantic UniversityĬontents 1 Lattice polygons 101 1.1 Pick’s Theorem: area of lattice polygon.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |