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Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
Mystery 7 from spain   2
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Mystery 7 from spain 2

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Mystery number 7 - 2 - from Spain, mathematics

Mystery number 7 - 2 - from Spain, mathematics

Published in: Education, Travel, Business
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Transcript

  • 1. MYSTERY #7 FROM SPAIN M
  • 2. WHOWAS I
  • 3. I WAS AMATHEMATICIAN
  • 4. I CREATED ALANGUAGE TO STUDY SYMMETRY
  • 5. I WAS KILLED IN A DUELWHEN I WAS ONLY TWENTY...
  • 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. 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. PART 2.WHATS SYMMETRY FOR ME? SYMMETRY IS MOTION.
  • 9. WHO WROTE THIS FAMOUS QUOTATION?
  • 10. IN THE ALHAMBRA OF GRANADA THERE IS SYMMETRYEVERYWHERE. IMMEDIATELY YOU GO IN, YOU SEE THEREFLECTIVE SYMMETRY IN THE WATER.
  • 11. BUT IT IS MOTION WHAT REALLY CHARACTERIZES THE SYMMETRYON WALLS, FLOORS AND DOMES INSIDE THE ALHAMBRA .
  • 12. HOW MANY TIMES CAN YOU MOVE A GEOMETRIC OBJECTAROUND A TURNIG POINT SO THAT IT LOOKS EXACTLYTHE 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 CLASSIFYALL THE POSSIBLE SYMMETRIESIN THE ALHAMBRA?CREATING A MATHEMATICAL LANGUAGE
  • 15. LETS TAKE A TWISTED SIX-POINTED STARFISH.WE CAN TURN THE STARA SIXTH OF A TURN, 1/6.
  • 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. 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. 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 LETS 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 THESETHINGS ARE ACTUALLY THE SAME,WITH THREE DIFFERENT AXIS OF ROTATION.
  • 21. LETS TAKE THIS WALL WITH THETWISTED TRIANGLES. THE SHAPESMATCH IF WE ROTATE 180º, HALF OF ATURN. IT HAS SYMMETRY NUMBER 2.
  • 22. A THIRD OF A TURN AROUND THE CENTRE OF THE TRIANGLEAND 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. LETS MOVE TO A DIFFERENT WALL. WE FIND THESAME SYMMETRIES.IT IS A SYMMETRY WE CALL 6-3-2.
  • 25. OUR MATHEMATICAL LANGUAGE ALLOWS US TO SAY THEYARE REPRESENTATIONS OF THE SAME ABSTRACTOBJECT.
  • 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. THE MYSTERY IS:M COULD YOU TELL US WHICH TYPE OF SYMMETRY IS THERE IN THIS PATTERN?
  • 28. WE HOPE YOU LIKE OUR MYSTERY
  • 29. THANK YOU VERY MUCH!

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