Mystery 7 from spain 2

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Mystery number 7 - 2 - from Spain, mathematics

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Mystery 7 from spain 2

  1. 1. MYSTERY #7 FROM SPAIN M
  2. 2. WHOWAS I
  3. 3. I WAS AMATHEMATICIAN
  4. 4. I CREATED ALANGUAGE TO STUDY SYMMETRY
  5. 5. I WAS KILLED IN A DUELWHEN I WAS ONLY TWENTY...
  6. 6. I COULD NOT SLEEP THAT NIGHT …I WAS SURE IT WAS MY LAST ONE..SO I SPENT THE WHOLE NIGHTWRITING MY MATHEMATIC WILL...
  7. 7. MY LAST WORDS TO MY BROTHER WERE,“DONT CRY FOR ME, ALFRED. I NEED ALL THE COURAGE I CAN MASTERTO DIE AT THE AGE OF 20”
  8. 8. PART 2.WHATS SYMMETRY FOR ME? SYMMETRY IS MOTION.
  9. 9. WHO WROTE THIS FAMOUS QUOTATION?
  10. 10. IN THE ALHAMBRA OF GRANADA THERE IS SYMMETRYEVERYWHERE. IMMEDIATELY YOU GO IN, YOU SEE THEREFLECTIVE SYMMETRY IN THE WATER.
  11. 11. BUT IT IS MOTION WHAT REALLY CHARACTERIZES THE SYMMETRYON WALLS, FLOORS AND DOMES INSIDE THE ALHAMBRA .
  12. 12. HOW MANY TIMES CAN YOU MOVE A GEOMETRIC OBJECTAROUND A TURNIG POINT SO THAT IT LOOKS EXACTLYTHE SAME AS BEFORE?
  13. 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. 14. PART 3.HOW TO CLASSIFYALL THE POSSIBLE SYMMETRIESIN THE ALHAMBRA?CREATING A MATHEMATICAL LANGUAGE
  15. 15. LETS TAKE A TWISTED SIX-POINTED STARFISH.WE CAN TURN THE STARA SIXTH OF A TURN, 1/6.
  16. 16. IF WE ROTATE THE YELLOW DOT FROMA TO B, WE CALL THIS SYMMETRYSIMPLY 6.WE USE THE CENTRE OF THE STARFISHAS THE ONLY AXIS.IF WE ROTATE THE DOT BY A THIRD OFA TURN, FROM A TO C, WE CALL IT 3, IT IS 1/3.
  17. 17. WE CAN ROTATE THE STAR A HALF OF ATURN, MOVING THE YELLOW DOT FROMA TO D.WE CALL THIS SYMMETRY 2,BECAUSE IT IS ½.
  18. 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. 19. WE CAN ROTATE THE STARFISH 360º,WE NAME THIS SYMMETRY WITH THE SYMBOL OF A STAR *. NOW LETS GO BACK TO THE WALLS OF THE ALHAMBRA
  20. 20. 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.
  21. 21. LETS TAKE THIS WALL WITH THETWISTED TRIANGLES. THE SHAPESMATCH IF WE ROTATE 180º, HALF OF ATURN. IT HAS SYMMETRY NUMBER 2.
  22. 22. A THIRD OF A TURN AROUND THE CENTRE OF THE TRIANGLEAND EVERYTHING MATCHES UP, IGNORING THE COLOURS. THIS IS SYMMETRY NUMBER 3.
  23. 23. FINALLY, THE SHAPES MATCH IF WE ROTATE BY A SIXTH OF A TURN.IT HAS SYMMETRIES 2, 3, 6 AND *
  24. 24. LETS MOVE TO A DIFFERENT WALL. WE FIND THESAME SYMMETRIES.IT IS A SYMMETRY WE CALL 6-3-2.
  25. 25. OUR MATHEMATICAL LANGUAGE ALLOWS US TO SAY THEYARE REPRESENTATIONS OF THE SAME ABSTRACTOBJECT.
  26. 26. DID THE MOORISH ARTISTS DICOVER ALL THE POSSIBLE SYMMETRIES ON THE SURFACES OF THE ALHAMBRA?THEY ALMOST DID. USING OUR LANGUAGE THEY ARE ONLY 17.
  27. 27. THE MYSTERY IS:M COULD YOU TELL US WHICH TYPE OF SYMMETRY IS THERE IN THIS PATTERN?
  28. 28. WE HOPE YOU LIKE OUR MYSTERY
  29. 29. THANK YOU VERY MUCH!

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