During the Medieval period, mathematics was used extensively in religion and art. Geometry was used in religious designs and symbols to represent concepts like the Holy Trinity. Mathematics was also an important part of the educational system through the seven liberal arts, which included the quadrivium of arithmetic, geometry, music, and astronomy. In art, the golden ratio and Fibonacci sequence appeared frequently in paintings, architecture, music, and poetry as representations of beauty and perfection.

1. MATHEMATICS DURING
THE MEDIEVAL PERIOD

2. 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.

3. Holy Trinity

4. cornerstones of
the temple

5. Wounds of Christ

10. Educational
System During
Medieval Period

11. The Seven Liberal Arts
The Trivium
and
The Quadrivium

12. The Trivium
Logic
Rhetoric
Latin Grammar

13. The Quadrivium
Arithmetic
Geometry
Music
Astronomy

14. 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

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

16. Geometry
Inspired by the 13 books of
Euclid’s Elements

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

18. 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.

19. Represented as:

20. 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

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

22. 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

23. 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.

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

27. 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.

28. 1.618…
1.61803398875…
The Golden Ratio
The Golden Mean
The Golden Number
The Divine Proportion
The Golden Proportion
The Divine Section

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

30. Golden Rectangle

31. Golden Spiral

32. The golden ratio
in some works of art

33. PAINTINGS

37. ARCHITECTURE

40. MUSIC

41. POETRY
Inspiration Comes
(Fibonacci)
by Jim T. Henriksen

42. 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.

43. COSMOLOGY

45. CONTEMPORARY LOGOS AND
DESIGNS