Mystery 7 from spain 2
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MYSTERY #7 FROM SPAINMYSTERY #7 FROM SPAINM
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WHO
WAS I
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I WAS
A MATHEMATICIAN
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I CREATED A LANGUAGE TO STUDY
SYMMETRY
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I WAS KILLED IN A DUEL WHEN I WAS ONLY TWENTY...
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I COULD NOT SLEEP THAT NIGHT …I WAS SURE IT WAS MY LAST ONE..SO I SPENT THE WHOLE NIGHT WRITING MY MATHEMATIC WILL...
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MY LAST WORDS TO MY BROTHER WERE, “DON'T CRY FOR ME, ALFRED. I NEED ALL THE COURAGE I CAN MASTER TO DIE AT THE AGE OF 20”
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PART 2. WHAT'S SYMMETRY FOR ME?
SYMMETRY IS MOTION.
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WHO WROTE THIS FAMOUS QUOTATION?
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IN THE ALHAMBRA OF GRANADA THERE IS SYMMETRY EVERYWHERE. IMMEDIATELY YOU GO IN, YOU SEE THE REFLECTIVE SYMMETRY IN THE WATER.
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BUT IT IS MOTION WHAT REALLY CHARACTERIZES THE SYMMETRY ON WALLS, FLOORS AND DOMES INSIDE THE ALHAMBRA .
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HOW MANY TIMES CAN YOU MOVE A GEOMETRIC OBJECT AROUND A TURNIG POINT SO THAT IT LOOKS EXACTLY THE SAME AS BEFORE?
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.
ON THE ALHAMBRA WALLS YOU CAN SEE THIS PATTERN. FIND A POINT WHERE YOU CAN TURN IT BY 90 DEGREES AND
IT KEEPS THE SAME
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PART 3. HOW TO CLASSIFY ALL THE POSSIBLE SYMMETRIESIN THE ALHAMBRA?CREATING A MATHEMATICAL LANGUAGE
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LET'S TAKE A TWISTED SIX-POINTED STARFISH.WE CAN TURN THE STAR A SIXTH OF A TURN, 1/6.
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IF WE ROTATE THE YELLOW DOT FROM A TO B, WE CALL THIS SYMMETRY SIMPLY 6.WE USE THE CENTRE OF THE STARFISHAS THE ONLY AXIS.IF WE ROTATE THE DOT BY A THIRD OF A TURN, FROM A TO C, WE CALL IT 3, IT IS 1/3.
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WE CAN ROTATE THE STAR A HALF OF A TURN, MOVING THE YELLOW DOT FROMA TO D. WE CALL THIS SYMMETRY 2, BECAUSE IT IS ½.
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IF WE TURN THE STAR FOUR-SIXTHSOF A TURN, 4/6, WE ROTATE THE
YELLOW DOT FROM A TO E.WE CALL IT 4.
IF WE ROTATE IT 5/6 OF A TURN, FROM A TO F, WE CALL IT 5
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WE CAN ROTATE THE STARFISH 360º,WE NAME THIS SYMMETRY WITH THE
SYMBOL OF A STAR *.NOW LET'S GO BACK TO THE
WALLS OF THE ALHAMBRA
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WE CAN SEE TWO VERY DIFFERENT PATTERNS, BUT USING OUR LANGUAGE,WE CAN UNDERSTAND THAT THE UNDERLYING ABSTRACT SYMMETRIES OF THESETHINGS ARE ACTUALLY THE SAME,WITH THREE DIFFERENT AXIS OF ROTATION.
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LET'S TAKE THIS WALL WITH THE TWISTED TRIANGLES. THE SHAPES MATCH IF WE ROTATE 180º, HALF OF A TURN. IT HAS SYMMETRY NUMBER 2.
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A THIRD OF A TURN AROUND THE CENTRE OF THE TRIANGLE AND EVERYTHING MATCHES UP, IGNORING THE COLOURS.
THIS IS SYMMETRY NUMBER 3.
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FINALLY, THE SHAPES MATCH IF WE ROTATE BY A SIXTH OF A TURN. IT HAS SYMMETRIES 2, 3, 6 AND *
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LET'S MOVE TO A DIFFERENT WALL. WE FIND THE SAME SYMMETRIES. IT IS A SYMMETRY WE CALL 6-3-2.
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OUR MATHEMATICAL LANGUAGE ALLOWS US TO SAY THEY ARE REPRESENTATIONS OF THE SAME ABSTRACT OBJECT.
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DID THE MOORISH ARTISTS DICOVER ALL THE POSSIBLESYMMETRIES ON THE SURFACES OF THE ALHAMBRA?
THEY ALMOST DID. USING OUR LANGUAGE THEY ARE ONLY 17.
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MTHE MYSTERY IS:
COULD YOU TELL US WHICH TYPEOF SYMMETRY IS THERE IN THIS PATTERN?
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WE HOPE YOU LIKE OUR MYSTERY
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THANK YOU VERY MUCH!