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Tessellations

MC Escher Fish Pattern

There are three different types of tessellations:

  • Regular
  • Semi-regular
  • Irregular

There are three ways to make regular tessellations:

  • Translation
  • Rotation
  • Reflection

Tessellation Slideshow

Translation is the simplest and easiest tessellating design to make. The congruent shape is slid in both horizontal and vertical directions inside the grid. The finished repeated design fits together without gaps or overlaps.

 

Rotation is a tessellating design where the congruent shape repeats around a central point. The finished design is repeated in a circular pattern inside the grid.

 

Reflection is a tessellating design where the congruent shape is repeated in a different method from a translation. The shape is repeated by sliding and flipping in both a horizontal and vertical directions inside the grid. The finished design fits together without gaps or overlaps.

Tessellations in Nature

Tessellations in Nature

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Three Lions – European Football

Threes in American Football

  • Three units on a football team; Offense, Defense, and Special Teams
  • Three ways of advancing a football; run, kick and pass
  • Three points for a field goal
  • In the football league the team that wins the game gets three points
  • In football you are allowed to call only 3 timeouts during each half of the game
  • Football’s 3-point stance

England football association - three lions crest
England football association – three lions crest

Threes in European Football

  • Three football teams in Glasgow – Celtic, Rangers & Partick Thistle
  • Three lions on an England football shirt (sorry, soccer shirt)
  • Three lines: Forwards, Halfback, Fullback

Three Lions” was the official song of the England football team for the 1996 European Championships, which were held in England. The music was written by The Lightning Seeds, with comedians David Baddiel and Frank Skinner providing the lyrics. The song was a much bigger success than most football songs, capturing the Zeitgeist perfectly.

Three Lions Footballs-Coming Home Official Video

The lyrics spoke not of unbounded optimism for victory, but instead told of how, ever since 1966 and the one unequivocal success of the English football team, every tournament has ended in dashed hopes and the feeling that England will never again reach those heights (“Three Lions on a shirt, Jules Rimet still gleaming Thirty years of hurt, never stopped me dreaming”).

The song’s intro included samples of pessimism from football commentators Alan Hansen (“I think it’s bad news for the English game”), Trevor Brooking (“We’re not creative enough; we’re not positive enough”), and Jimmy Hill (“We’ll go on getting bad results”).

Despite the failures of the past, each tournament is greeted with fresh hopes that this might be the year they do it again, and the song’s exuberant chorus proclaimed that “It’s coming home, it’s coming home, it’s coming, football’s coming home”.

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Monty Python and the Holy Grail – thou must count to three

A reading from the Book of Armaments, Chapter 4, Verses 16 to 20:

Then did he raise on high the Holy Hand Grenade of Antioch, saying, “Bless this, O Lord, that with it thou mayst blow thine enemies to tiny bits, in thy mercy.” And the Lord did grin, and the people did feast upon the lambs and toads and tree-sloths and fruit-bats and orangutans and breakfast cereals …

Now did the Lord say, “First thou pullest the Holy Pin. Then thou must count to three. Three shall be the number of the counting and the number of the counting shall be three. Four shalt thou not count, neither shalt thou count two, excepting that thou then proceedeth to three. Five is right out.

Once the number three, being the number of the counting, be reached, then lobbest thou the Holy Hand Grenade in the direction of thine foe, who, being naughty in my sight, shall snuff it.”

Clip

Monty Python-Holy Hand Grenade

Monty Python

Monty Python were a British comedy troupe formed in 1969 consisting of Graham Chapman, John Cleese, Terry Gilliam, Eric Idle, Terry Jones, and Michael Palin. The group came to prominence for the sketch comedy series Monty Python’s Flying Circus, which aired on the BBC from 1969 to 1974.