# 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

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## 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