Module 8

• Ludwick Van Beethoven

  • a deaf musician who relies on mathematics pattern to write melodies
  • consonance and dissonance
• consonance: harmony, agreement, pleasing to ear
• dissonance: tension, conflict
• Ndugu Chancler

  • combination of sounds and spaces
  • multiplication, addition, division
• Dr. James Steward

  • best-selling calculus
  • violinist
  • music + math: those who are exceptionally good in math are also drawn to music
  • science, medicine, math, engineering
• Music is the abstract of art, while math is the abstract of science
• Geometric Transformation

  • Translation - Transposition
  • Reflection about a horizontal axis - Inversion
  • Reflection about a vertical axis - retrogression
  • Rotation about 180 degrees - Retrograde Inversion
  • Dilation with scale factor greater than 1 - augmentation (twice as slowly)
  • Dilation with scale factor less than 1 - diminution (twice as quickly)
• Johann Sebastian Bach

  • Translation
  • Rotation
  • Reflection
• Douglas R. Hofstadter

  • musical theme is played backward
  • bach, escher, godel
• M.C. Escher: Crab Canon
• Dance: geometry in motion
• Synchronization: dancers count their steps according to the rhythm of the music they are dancing to
• Shapes: dancers form shapes and angles with their body for choreography
• Spatial Awareness: dancers must maintain their position and formation especially in group choreography
• Symmetry : Dancers have to make sure that they reflect the same pattern as their fellow dancers for them to be synchronized and appear as one
• Precision: the exactitude of dance makes it professional. Each movement and step is measured out purposefully
• Principles of Math in Dance

  • Geometry
  • Time
  • Physics
  • Patterns
• Direction: Line of movement made while moving in space
• Level: Height of the dancer in relation to the floor
• Range: The area covered as the body moves
• Floor / Space Pattern: The path or design on floor/in space that is made while moving in space
• • Translation: Sliding Symmetry
  • Reflection: Mirror Symmetry
  • Rotation: turning Symmetry
  • Glide : Slide and Mirror Symmetry
• Weaving is used for

  • Practical Purposes
  • Tradition & Ceremonies
  • Expression of One's social statues; religious beliefs, achievements
• Repetition: basic discreet element found in a woven textile
• Finite Symmetrical Design: obtained by a repetition of motif
• Frieze Pattern: Repeating pattern admits translations in one direction
• Wallpaper Pattern: admits translations in two directions
• Sablay: weaver of Arevalo Iloilo

  • sinuksok method
  • Translation and Glide Reflection
• Pisyabit: Tausugs of Sulu
• Architecture

  • both functional and aesthetic advantages
  • directly associated with math
• geometry: serves as the foundational principle
• Golden ratio: used to create structures that are visually appealing, harmonious and balanced
• Algebra: integral for determining and optimizing material quantities
• Trigonometry: Ensures structural ability
• San Miguel Corporation Building

  • Banaue Rice Terraces
  • Stairway to Sky
• Taj Mahal: golden ratio
• Grand Egyptian Museum: fractal geometry was employed to create intricate patterns
• Poems with patterns

  • counting: numerical features as the skeletal structure
  • constraint: rules that integrate mathematical components
• Traditional Poem: 10 syllables

  Japanese Haiku: 5 - 7 - 5

  Fibonacci Poem: words and syllables
• Tagalog's Balagtasan: manner of debate that uses poetic elements