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1ST SEMESTER: BSBA MM > Mathematics in the Modern World: Lecture 1 and 2 > Flashcards

Mathematics in the Modern World: Lecture 1 and 2 Flashcards

(55 cards)

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1
Q

He mentioned that we live in a universe of patterns.

A

Ian Stewart

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2
Q

These are the things that are repetitive, which can be found in nature as color, shape, action, or some other sequences that are almost everywhere.

A

Patterns

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3
Q

It is a way to calculate or solve a problem.

A

Rule

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4
Q

It expresses patterns.

A

Mathematics

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5
Q

It is an exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis.

A

Symmetry

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6
Q

It is also called mirror symmetry or line symmetry.

A

Reflection Symmetry

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7
Q

Reflection Symmetry is also called as, what?

A

Mirror Symmetry or Line Symmetry

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8
Q

It is also called radial symmetry.

A

Rotational Symmetry

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9
Q

Rotational Symmetry is also called as, what?

A

Radial Symmetry

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10
Q

In Biology, this kind of symmetry is exhibited by objects when their similar parts are regularly arranged around a central axis and the pattern looks the same after a certain amount of rotation. Note that if you rotate the given images below by several degrees, you can still
achieve the same appearance as the original position.

A

Rotation Symmetry

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11
Q

This kind of symmetry is exhibited by objects which do not change its size and shape even if it moved to another location. Note that the movement does not involve with reflection or rotation.

A

Translational Symmetry

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12
Q

What are the kinds of symmetry?

A

Reflection Symmetry; Rotational Symmetry; Translational Symmetry

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13
Q

These are never-ending patterns that are self-similar across different scales. The image just reappears over and over again no matter how
many times the object is magnified.

A

Fractals

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14
Q

Patterns are also exhibited in the external
appearances of animals.

A

Spots and Stripes

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14
Q

These are curved patterns made by series

A

Spirals

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15
Q

Flowers are easily considered as things of beauty.
Their vibrant colors and fragrant odors make them
very appealing as gifts or decorations.

A

Flower Petals

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16
Q

Are easily considered as things of beauty.

A

Flowers

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16
Q

What are the types of patterns in nature?

A

Symmetry; Spiral; Fractals; Spots and Stripes; Flower Petals

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17
Q

It is a series of numbers where a
number is found by adding up the two numbers before it.

A

Fibonacci Sequence

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18
Q

The sequence encountered in the rabbit problem 1,
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, … is
called the _________.

A

Fibonacci Sequence

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18
Q

The terms in the Fibonacci sequence is called _________.

A

Fibonacci Numbers

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19
Q

He is also known as Fibonacci

A

Leonardo of Pisa

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20
Q

It is the perfect rectangle.

Study These Flashcards
A

Golden Rectangle

21
Q

The golden ratio was first called as the ___________ in the early
1500s

Study These Flashcards
A

Divine Proportion

21
It was first called as the Divine Proportion
Golden Ratio
22
This contains the drawings of the five platonic solids and it was probably da Vinci.
De Divina Proportione
23
The drawings of five platonic solids is called, what in Latin?
Section aurea or Golden Secion
24
What is the formula of the golden ratio?
25
The number of petals in a flower is often one of the following numbers: 3, 5, 8, 13, 21, 34 or 55. For example, the lily has three petals, buttercups have five of them, the chicory has 21 of them, the daisy has often 34 or 55 petals, etc.
Flower Petals
26
In Fibonacci, written as a rule the expression is...
27
In both human and nonhuman, abound with examples of the Golden Ratio. The mouth and nose are each positioned at golden sections of the distance between the eyes and the bottom of the chin. Similar proportions can been seen
Faces
28
These are produced at the center, and then migrate towards the outside to fill all the space. Sunflowers provide a great example of these spiraling patterns.
Seed Heads
28
The Golden Section is manifested in the structure of the human body. The human body is based on Phi and the number 5.The number 5 appendages to the torso, in the arms, leg and head. 5 appendages on each of these, in the fingers and toes and 5 openings on the face. Animal bodies exhibit similar tendencies.
Body Parts
28
Spiraling patterns can be found on pineapples and cauliflower. Fibonacci numbers are seen in the branching of trees or the number of leaves on a floral stem; numbers like 4 are not. 3’s and 5’s, however, are abundant in nature.
Fruits, Vegetables, and Trees
29
These are the most common galaxy shape. The Milky Way has several spiral arms, each of them a logarithmic spiral of about 12 degrees.
Spiral Galaxies
30
It follow the logarithmic spiral, as does the cochlea of the inner ear. It can also be seen in the horns of certain goats, and the shape of certain spider’s webs.
Shells
31
It’s amazing how closely the powerful swirls of ________ match the Fibonacci sequence.
Hurricanes
32
The exterior dimension of the ___________ in Athens, Greece embodies the golden ratio.
Pathernon
33
Here, Plato describes five possible regular solids that relate to the golden ratio which is now known as Platonic Solids.
Timaeus
34
He 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”.
Euclid
35
He was into many interests such as invention, painting, sculpting, architecture, science, music, mathematics, engineering, literature, anatomy, geology, botany, writing, history and cartography. He used the golden ratio to define the fundamental portions in his works. He incorporated the golden ratio in his own paintings such as the Vitruvian Man, The Last Supper, Monalisa and St. Jerome in the Wilderness.
Leonardo Da Vinci
36
It is “a dividing line in the extreme and mean ratio” in his book the “Elements”.
Golden Ratio
37
He was considered the greatest living artists of his time. He used golden ratio in his painting “The Creation of Adam” which can be seen on the ceiling of the Sistine Chapel. His painting used the golden ratio showing how God’s finger and Adam’s finger meet precisely at the golden ratio point of the weight and the height of the area that contains them.
Michaelangelo di Lodovico Simon
38
More popularly known as Raphael was also a painter and architect from the Rennaisance. In his painting “The School of Athens,”, the division between the figures in the painting and their proportions are distributed using the golden ration. The golden triangle and pentagram can also be found in Raphael’s painting “Crucifixion”.
Raffaello Sanzio da Urbino
39
In his work “The Sacrament of the Last Supper”, golden ratio can be found.
Salvador Dali
40
In his works(“Bathers at Assinieres”, “Bridge of Courbevoie” and “A Sunday on La Grande Jette”, golden ratio can be found.
George-Pierre Surat
41
In his work “Birth of Venus”, golden ratio can be found.
Sandro Botticelli
42
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.
Great Pyramid of Giza
43
Is a Gothic Cathedral in Paris, which was built in between 1163 and 1250. It appears to have a golden ratio in a number of its key proportions of designs.
Notre dame
44
The _________ in India used the golden ratio in its construction and was completed in 1648. The order and proportion of the arches of the _______ on the main structure keep reducing proportionately following the golden ratio.
Taj Mahal
45
The _______ in Paris, France also exhibits the Golden ratio.
Cathedral of Our Lady of Chartres
46
In the ________, the window configuration reveal golden proportion
United Nation Building
47
The __________ in Paris, France, erected in 1889 is an iron lattice. The base is broader while it narrows down the top, perfectly following the golden ratio.
Eiffel Tower
48
The _______ in Toronto, the tallest tower and freestanding structure in the world, contains the golden ratio in its design. The ratio of observation deck at 342 meters to the total height of 553.33 is 0.618 or phi, the reciprocal of phi.
CN Tower
49
The five possible regular solids is now called what?
Platonic Solids

1ST SEMESTER: BSBA MM (10 decks)

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