mystery 7 from spain 2

MYSTERY #7 FROM SPAINMYSTERY #7 FROM SPAINM

WHO

WAS I

I WAS

A MATHEMATICIAN

I CREATED A LANGUAGE TO STUDY

SYMMETRY

I WAS KILLED IN A DUEL WHEN I WAS ONLY TWENTY...

I COULD NOT SLEEP THAT NIGHT …I WAS SURE IT WAS MY LAST ONE..SO I SPENT THE WHOLE NIGHT WRITING MY MATHEMATIC WILL...

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”

PART 2. WHAT'S SYMMETRY FOR ME?

SYMMETRY IS MOTION.

WHO WROTE THIS FAMOUS QUOTATION?

IN THE ALHAMBRA OF GRANADA THERE IS SYMMETRY EVERYWHERE. IMMEDIATELY YOU GO IN, YOU SEE THE REFLECTIVE SYMMETRY IN THE WATER.

BUT IT IS MOTION WHAT REALLY CHARACTERIZES THE SYMMETRY ON WALLS, FLOORS AND DOMES INSIDE THE ALHAMBRA .

HOW MANY TIMES CAN YOU MOVE A GEOMETRIC OBJECT AROUND A TURNIG POINT SO THAT IT LOOKS EXACTLY THE SAME AS BEFORE?

.

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

PART 3. HOW TO CLASSIFY ALL THE POSSIBLE SYMMETRIESIN THE ALHAMBRA?CREATING A MATHEMATICAL LANGUAGE

LET'S TAKE A TWISTED SIX-POINTED STARFISH.WE CAN TURN THE STAR A SIXTH OF A TURN, 1/6.

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.

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.

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

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

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.

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.

A THIRD OF A TURN AROUND THE CENTRE OF THE TRIANGLE AND EVERYTHING MATCHES UP, IGNORING THE COLOURS.

THIS IS SYMMETRY NUMBER 3.

FINALLY, THE SHAPES MATCH IF WE ROTATE BY A SIXTH OF A TURN. IT HAS SYMMETRIES 2, 3, 6 AND *

LET'S MOVE TO A DIFFERENT WALL. WE FIND THE SAME SYMMETRIES. IT IS A SYMMETRY WE CALL 6-3-2.

OUR MATHEMATICAL LANGUAGE ALLOWS US TO SAY THEY ARE REPRESENTATIONS OF THE SAME ABSTRACT OBJECT.

DID THE MOORISH ARTISTS DICOVER ALL THE POSSIBLESYMMETRIES ON THE SURFACES OF THE ALHAMBRA?

THEY ALMOST DID. USING OUR LANGUAGE THEY ARE ONLY 17.

MTHE MYSTERY IS:

COULD YOU TELL US WHICH TYPEOF SYMMETRY IS THERE IN THIS PATTERN?

WE HOPE YOU LIKE OUR MYSTERY

THANK YOU VERY MUCH!