Category Archives: Mathematics
The Theorem of Trithagoras; Pythagoras is for Squares. The MathsJam 2017 Five-minute Presentation.
Mention Pythagoras and Pythagorean triangles spring to mind, but his theorem is really about the area of certain squares (regular polygons with four sides) and sums of their areas, which happens to relate to the sides of the aforesaid triangles. … Continue reading
Tessellating the Hardy-Ramanujan Taxicab Number, 1729, Bedrock of Integer Sequence A198775.
Here is Trefoil Lattice Labyrinth (32,15). There’s something rather special about it. According to the celebrated story, the English mathematician G.H.Hardy arrived at the hospital bedside of his Indian protege ( the autodidact mathematical genius) Srinivasa Ramanujan in London taxi … Continue reading
Tessellatable Numbers up to 2100, with corresponding Gaussian and Loeschian Number Pairs
The following tables, which should appeal to your inner nerd and might even be USEFUL, pick out which integers N in the range 1 to 2100 are of the form a²+b² and/or of the form e²+ef+f². The first category are … Continue reading
Fibonacci puts the Pee in Pisa – Light Relief for the Also-wrangled
Etiam mingens mathematicae memini! As you probably know only too well, in a Fibonacci Sequence of numbers, each successive term is the sum of the two preceding terms, so all you need to do to start it off is specify … Continue reading
Pythagorean Pairs of Pairs…and the Occasional Triplet of Pairs
Here are small parts of two Serpentine Lattice Labyrinth tessellations. Though these two patterns look very different and the arrays of superlattice points (which we can take to be marked by the black squares) and symmetry axes are at different … Continue reading
Eine nicht so kleine Mathmusik: from Lattice Labyrinths to Integer-sided Trythagorean Triangles
Revision: In the previous post we investigated “squaring” a lattice labyrinth tessellation, multiplying the tessellation by itself and by its mirror image. This is equivalent to multiplying number pairs (a,b) x (a,b) and (a,b) x (b,a) where (a,b) are the … Continue reading
Eine kleine Mathmusik : From Lattice Labyrinths via √-1 to Pythagorean Triples
Since starting this blog I have made a point of “following” twitter accounts maintained by passionate mathematics teachers and many have paid me the complement of following me in return. It is time I thanked them/you for this complement by … Continue reading
Eureka Moments, a Downer from Dennis Sciama and Dinner with Fred Hoyle
While The Theory of Everything , the Stephen Hawking biopic film, is topical, I interrupt this blog, which is the outcome of one Eureka Moment, to tell you the tale of another such experience. This Eureka Moment was concerned with … Continue reading
Lattice Labyrinths Bridges Conference Paper 12
Warning – hard numerate thinking to be thunk. I’m most honoured to have had a paper accepted for this August’s Bridges Conference in Seoul, Republic of Korea. At eight pages, it has only about one sixth the surface area of … Continue reading
Great Triangular Tessellations!
Birthdate Years that may be Supertile areas of Trefoil or Honeycomb Labyrinths Trefoil Labyrinths have supertitle area, S = (e2 + ef + f2), so we are looking for e and f that give (e2 + ef + f2) equal … Continue reading
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