{"id":18185,"date":"2013-02-07T23:41:50","date_gmt":"2013-02-07T22:41:50","guid":{"rendered":"http:\/\/thomasjpitts.co.uk\/wp\/?p=18185"},"modified":"2013-02-07T23:41:50","modified_gmt":"2013-02-07T22:41:50","slug":"day-38-rotational-symmetry","status":"publish","type":"post","link":"https:\/\/thomasjpitts.co.uk\/wordpress\/2013\/02\/07\/day-38-rotational-symmetry\/","title":{"rendered":"Day 38: Rotational Symmetry"},"content":{"rendered":"

Today my brain was stuck in rotational symmetry mode, spotting it everywhere.<\/p>\n

A few years ago I stumbled upon hub caps on cars and their general properties of rotational symmetry (if you ignore the air nozzle and central logos…)<\/p>\n

\"Rotational<\/a><\/p>\n

These are good for demonstrating how a pattern can be laid over itself to create intricate patterns. With Rotational Symmetry<\/a>, the shape or image can be rotated and it still looks the same.\u00a0How many matches\u00a0there are as you go once around\u00a0is called the order.In our staff car park, there were no two sets of hub caps the same – interesting in itself really.<\/p>\n

\"Some<\/a>
Some hub caps. Yesterday.<\/figcaption><\/figure>\n

Each of the ones above are different designs, and left to right, have orders of rotational symmetry of 5, 5, and 7. We found ones with 9, 11, 8, 6, and the steering wheel of Mr Rhodes’ car had an order of 2!<\/p>\n

If a shape only matches itself once\u00a0as you go around (i.e. it only matches itself after one full rotation<\/a>) there is really no symmetry at all, because the word “Symmetry” comes from\u00a0syn-\u00a0together<\/b>\u00a0<\/i>and\u00a0metron\u00a0measure<\/b>,\u00a0<\/i>and there can’t be “together” if there is just one thing.<\/p>\n

Other good examples of rotation symmetry are dart boards, a star and the London Eye<\/a>.<\/p>\n

\"A<\/a>
A tournament dartboard with an order of symmetry of 10.<\/figcaption><\/figure>\n
\"A<\/a>
A star with an order of rotational symmetry of 5.<\/figcaption><\/figure>\n
\"The<\/a>
The London Eye with an order of symmetry of 32.<\/figcaption><\/figure>\n

My head still isn’t great. Been taking migraine tables to ward it off all day and as I type I’m getting very drowsy from pain behind my eyes. Sleep once more beckons.<\/p>\n

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