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Information about Medieval mathematics

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MATHEMATICS IN RELIGION • Geometry is used in the developments of some religious designs used during that time which some are even used until today. By infusing Mathematics, their works of art became full of symbolisms and meanings. During Medieval times, people use different geometric symbols to defy their religious ideas and beliefs as much as words do.

Holy Trinity

cornerstones of the temple

Wounds of Christ

Educational System During Medieval Period

The Seven Liberal Arts The Trivium and The Quadrivium

The Trivium Logic Rhetoric Latin Grammar

The Quadrivium Arithmetic Geometry Music Astronomy

The Quadrivium Arithmetic (Number in itself) - as such number is a pure abstraction outside of time and space. This aspect of the Quadrivium deals with the different characteristics of each number

The Quadrivium Geometry (Number in space) - specific shapes can have a deeper meaning. This aspect relates symbolism and it is frequently used in architecture

Geometry Inspired by the 13 books of Euclid’s Elements

The Quadrivium Music (Number in time) - covers music in general and particularly the topic of natural harmonics

Golden Ratio • two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

Represented as:

Other term for Golden Ratio • • • • • • • • • golden section golden mean extreme and mean ratio medial section divine proportion divine section golden proportion golden cut golden number

Golden Ratio in Music •As a musical interval the ratio 1.618...

The Quadrivium Astronomy (Number in time and space) - covers the movement of planets in space and the natural harmonics between the planets when looking at the aspect of time (harmony of the spheres). This is the first time aspects of time and space meet with the abstraction of number thus it builds the foundation for science

Astronomy • During the medieval period, scientists in the Islamic world made many contributions to the field of astronomy. While their work was based on ancient sources from Greece, Iran, and India, they updated methods for measuring and calculating the movement of heavenly bodies, and continued to develop models of the universe and the movements of the planets within it.

Mathematics in ART “Without Mathematics, there is no art.” – Luca Pacioli

Take a look at the Fibonacci Sequence… 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89… Try getting the ratio between one of the numbers and the number before it.

1.618… 1.61803398875… The Golden Ratio The Golden Mean The Golden Number The Divine Proportion The Golden Proportion The Divine Section

We use Phi (ϕ) and phi (φ) to denote the Golden Ratio and its reciprocal respectively

Golden Rectangle

Golden Spiral

The golden ratio in some works of art

PAINTINGS

ARCHITECTURE

MUSIC

POETRY Inspiration Comes (Fibonacci) by Jim T. Henriksen

Inspiration Comes (Fibonacci) by Jim T. Henriksen I am sitting quietly, listening for the quiet noises in the darkness, ghostly images flying between the tall pine trees, illusion created by the mind, made by shadows, the brain playing tricks on itself. It sits there, the raven, black as night, looking at me with its dark eyes in the dark night. Inspiration comes. Words form in my head. Nevermore.

COSMOLOGY

CONTEMPORARY LOGOS AND DESIGNS

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