# Tag Archives: Loeschian

## Tiptoe tentatively into tessellated 2017

HURRAH!  2017 is the first tessellatable year since 2011, either on the square or on the triangular lattice. To start with the last but best image I’ve found: This shows symmetry axes and six supertiles of Trefoil Lattice Labyrinth (41,7), … Continue reading

## A Lattice Labyrinth for Cristián: Trefoil (29,3)

Cristian is a correspondent in Chile who helped spread the word of my abortive but world-wide 2012 campaign for an Olympic Fourth Place Medal. Cristián’s special date is 29th. March, so here, as a belated thank you, is Trefoil Lattice … 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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## 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

## Chinese National Day Tessellation applied to Shenzhen Bao’an International Airport 国庆节深圳宝安国际机场

Diamond Lattice Labyrinth (10,1) in honour of the National Day of The People’s Republic of China is illustrated in the previous post. I would like to employ it as a paving in Shenzhen City, where my elder son lives and … Continue reading

## On the Eve of 1st. October, the National Day of the People’s Republic of China 国庆节

I have been made very welcome both in the  People’s Republic of China and in Hong Kong, so, still just within 30th. September British time,but already early in the morning, Chinese Time, of what I do hope will be a … Continue reading

## Better World Cup Consolation Tessellations

I’m not sure that the Lattice Labyrinths suggested for Brazil and Argentina are worthy of those great countries.  Here is another, less conventional realisation of Serpentine (9,7) and Serpentine (7,9) in national flag colours. The supertiles are much bolder in form. … Continue reading

## Consolation Tessellations for Brazil and Argentina

Thank you to today’s visitor to this blog from Brazil and best wishes to the inspiring neuro-psychologist from Rio de Janeiro who visited the Celebrating Cromford festival on Saturday 21st. June this year. Not only Brazil, but now also Argentina … Continue reading

## Illustrated Talk at Scarthin Books, Cromford, Derbyshire

I’ll be giving an illustrated talk on Lattice Labyrinth Tessellations in the Bookshop Cafe on Saturday 12th. July, 2014. There will be a break for a light buffet (free but small donations welcomed). This is a meeting in Scarthin Books’ … Continue reading

## A Tessellation for the World Cup – A Labyrinth with Brio for Rio

Before I reveal a zestful tessellation in honour of the 2014 World Cup competition, here is the basic tessellation (the lowest-order member) of the Dart Lattice Labyrinth family. The lower part of the diagram is the complementary or missing-links graph, … Continue reading