10. IN THE ALHAMBRA OF GRANADA THERE IS SYMMETRY
EVERYWHERE. IMMEDIATELY YOU GO IN, YOU SEE THE
REFLECTIVE SYMMETRY IN THE WATER.
11. BUT IT IS MOTION WHAT REALLY CHARACTERIZES THE SYMMETRY
ON WALLS, FLOORS AND DOMES INSIDE THE ALHAMBRA .
12. HOW MANY TIMES CAN YOU MOVE A GEOMETRIC OBJECT
AROUND A TURNIG POINT SO THAT IT LOOKS EXACTLY
THE SAME AS BEFORE?
13. 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
.
14. PART 3.
HOW TO CLASSIFY
ALL THE POSSIBLE SYMMETRIES
IN THE ALHAMBRA?
CREATING A MATHEMATICAL LANGUAGE
15. LET'S TAKE A TWISTED SIX-
POINTED STARFISH.
WE CAN TURN THE STAR
A SIXTH OF A TURN, 1/6.
16. IF WE ROTATE THE YELLOW DOT FROM
A TO B, WE CALL THIS SYMMETRY
SIMPLY 6.
WE USE THE CENTRE OF THE STARFISH
AS 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.
17. WE CAN ROTATE THE STAR A HALF OF A
TURN, MOVING THE YELLOW DOT FROM
A TO D.
WE CALL THIS SYMMETRY 2,
BECAUSE IT IS ½.
18. IF WE TURN THE STAR FOUR-SIXTHS
OF 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
19. 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
20. WE CAN SEE TWO VERY DIFFERENT PATTERNS, BUT USING OUR LANGUAGE,
WE CAN UNDERSTAND THAT THE UNDERLYING ABSTRACT SYMMETRIES OF THESE
THINGS ARE ACTUALLY THE SAME,WITH THREE DIFFERENT AXIS OF ROTATION.
21. 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.
22. A THIRD OF A TURN AROUND THE CENTRE OF THE TRIANGLE
AND EVERYTHING MATCHES UP, IGNORING THE COLOURS.
THIS IS SYMMETRY NUMBER 3.
23. FINALLY, THE SHAPES MATCH
IF WE ROTATE BY A SIXTH OF A TURN.
IT HAS SYMMETRIES 2, 3, 6 AND *
24. LET'S MOVE TO A DIFFERENT WALL. WE FIND THE
SAME SYMMETRIES.
IT IS A SYMMETRY WE CALL 6-3-2.