WorksheetsModule 1: Nature of Mathematics
Total questions: 36
Worksheet time: 33mins
organize and systematize ideas about patterns in nature.
Mathematics
Nature
Science
Numbers
Around 1200 AD he published the Liber Abbaci, or “Book of Calculation.” An arithmetic text on financial computations and promoted the use of Hindu-Arabic numerals.
(a)
the sequence f1, f2, f3, f4, … which has its first two terms f1 and f2 both equal to 1 and satisfies thereafter the recursion formula fn = fn–1 + fn–2.
(a)
can be broken into squares the size of the next Fibonacci number down and below.
golden rectangle
golden triangle
golden circle
golden square
Take a golden rectangle, break it down into smaller squares based from Fibonacci sequence and divide each with an arc.
Fibonacci Spiral
Fibonacci
Fibonacci Sequence
Fibonacci Pattern
found the relationship between Fibonacci sequence and the golden ratio.
(a)
the relationship between numbers on the Fibonacci sequence where plotting the relationships on scales results in a spiral shape
(a)
The Fibonacci numbers can be applied to the proportions of a rectangle
(a)
A Fibonacci spiral which approximates the golden spiral, using Fibonacci sequence square sizes up to .
30
31
32
33
34
the limit of the ratios of successive terms of the Fibonacci sequence (or any Fibonacci-like sequence), as originally shown by Johannes Kepler (1571–1630).
(a)
The golden ratio is the limit of the ratios of successive terms of the Fibonacci sequence (or any Fibonacci-like sequence), as originally shown by (a) (1571–1630).
Also known as Golden Section, or Golden Proportion, or Divine Proportion denoted by Phi (ϕ) =
(a)
widely used the golden ratio in his works of sculpture. The exterior dimension of the Parthenon in Athens, Greece embodies the golden ratio.
(a)
In “Timaeus” (a) (428 BC – 347 BC) describes five possible regular solids that relate to the golden ratio. He also considers the golden ratio to be the most binging of all mathematic relationships.
was the first to give definition of the golden ratio as “a dividing line in the extreme and mean ratio” in his book the “Elements.”
He proved the link of the number to the construction of the pentagram, known as golden ratio.
(a)
(1452–1519) or known as Leonardo da Vinci was into invention, painting, sculpting, architecture, science, music, mathematics, engineering, literature, anatomy, geology, astronomy, botany, writing, history, and cartography.
(a)
(1475–1564) or known as Michelangelo was a painter, architect, poet, and engineer from the Renaissance.
He was considered the greatest living artist of his time.
(a)
(1483–1520) or known as Raphael was also a painter and architect from the Renaissance.
(a)
(1606–1669) or simply known as Rembrandt is a Dutch painter. It is said that the golden triangle is applied in his paintings “Self Portrait”.
(a)
(1445–1510), known as Sandro Botticelli, is an Italian painter.
The Birth of Venus is one of the world’s famous and appreciated works of art and it was painted between 1482 and 1485.
(a)
(1859–1891) was a French post-impressionist painter.
His paintings appear to have applied golden ratio to define the horizon, to place point of interest and to create balance.
(a)
(1904–1989) or known as Salvador Dali framed his paintings using the golden ratio in his masterpiece, “The Sacrament of the Last Supper.”
(a)
It was built 4700 BC in Ahmes Papyrus of Egypt is with proportion according to a “Golden Ratio.”
The length of each side of the base is 756 feet with a height of 481 feet.
The ratio of the base to the height is roughly 1.5717, which is close to the Golden ratio.
(a)
a Gothic Cathedral in Paris, built in between 1163 and 1250.
(a)
In India, used the golden ratio in its construction and was completed in 1648.
(a)
In Paris, France also exhibits the golden ratio.
(a)
the window configuration reveal golden proportion.
(a)
In Paris, France, erected in 1889 is an iron lattice.
(a)
In Toronto, the tallest tower and freestanding structure in the world, contains the golden ratio in its design.
(a)
a sense of harmonious and beautiful proportion of balance or an object is invariant to any of various transformations (reflection, rotation or scaling).
(a)
a symmetry in which the left and right sides of the organism can be divided into approximately mirror image of each other along the midline.
Bilateral symmetry
Radial symmetry
(or rotational symmetry) is a type of symmetry around a fixed point known as the center and it can be classified as either cyclic or dihedral.
Bilateral symmetry
Radial symmetry
a curve or geometric figure, each part of which has the same statistical character as the whole.
(a)
A (a) (or growth spiral) is a self-similar spiral curve which often appears in nature.
Age of the trees can be determined by applying (a) which is a scientific method of dating based on the amount of rings found in the core of a tree.
Turtles have growth rings called “ (a) ” which are hexagonal. It estimates the age of the turtle.
