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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

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.

A

Golden Rectangle

21
Q

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

A

Divine Proportion

21
Q

It was first called as the Divine Proportion

A

Golden Ratio

22
Q

This contains the drawings of the
five platonic solids and it was probably da Vinci.

A

De Divina Proportione

23
Q

The drawings of five platonic solids is called, what in Latin?

A

Section aurea or Golden Secion

24
Q

What is the formula of the golden ratio?

A
25
Q

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.

A

Flower Petals

26
Q

In Fibonacci, written as a rule the expression is…

A
27
Q

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

A

Faces

28
Q

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.

A

Seed Heads

28
Q

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.

A

Body Parts

28
Q

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.

A

Fruits, Vegetables, and Trees

29
Q

These are the most common
galaxy shape. The Milky Way has several
spiral arms, each of them a logarithmic
spiral of about 12 degrees.

A

Spiral Galaxies

30
Q

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.

A

Shells

31
Q

It’s amazing how closely the powerful
swirls of ________ match the Fibonacci
sequence.

A

Hurricanes

32
Q

The exterior dimension of the
___________ in Athens, Greece
embodies the golden ratio.

A

Pathernon

33
Q

Here, Plato describes five
possible regular solids that relate
to the golden ratio which is now
known as Platonic Solids.

A

Timaeus

34
Q

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”.

A

Euclid

35
Q

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.

A

Leonardo Da Vinci

36
Q

It is “a dividing line in the extreme
and mean ratio” in his book the “Elements”.

A

Golden Ratio

37
Q

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.

A

Michaelangelo
di
Lodovico
Simon

38
Q

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”.

A

Raffaello Sanzio da Urbino

39
Q

In his work “The Sacrament of the Last Supper”, golden ratio can be found.

A

Salvador Dali

40
Q

In his works(“Bathers at Assinieres”, “Bridge of Courbevoie” and “A Sunday on
La Grande Jette”, golden ratio can be found.

A

George-Pierre Surat

41
Q

In his work “Birth of Venus”, golden ratio can be found.

A

Sandro Botticelli

42
Q

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

Great Pyramid of Giza

43
Q

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.

A

Notre dame

44
Q

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.

A

Taj Mahal

45
Q

The _______ in Paris, France also
exhibits the Golden ratio.

A

Cathedral of Our Lady of Chartres

46
Q

In the ________, the window configuration reveal
golden proportion

A

United Nation Building

47
Q

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.

A

Eiffel Tower

48
Q

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.

A

CN Tower

49
Q

The five possible regular solids is now called what?

A

Platonic Solids

1ST SEMESTER: BSBA MM (10 decks)

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