MATHEMATICS IN MODERN WORLD (Prelim coverage)

Question 1

Conventions on Writing Sets

Answer 1

SYMMETRY

Question 2

is a curve which emanates from a
point, moving farther away as it revolves
around the point. In the natural world, we
find spirals in the DNA double helix,
sunflowers, the path of draining water,
weather patterns (including hurricanes),
vine tendrils, phyllotaxis (the arrangement
of leaves on a plant stem), galaxies, the
horns of various animals, mollusc shells,
the nautilus shell, snail shells, whirlpools, ferns and algae.

Answer 2

SPIRAL

Question 3

is one which
refers to a winding curve or bend in a
river. Are typical landforms
at the middle and lower courses of a
river.

Answer 3

MEANDER

Question 4

Is a physical phenomenon characterized by its frequency, wavelength,
and amplitude. In general, transfer energy from one location to another, in
which case they have a velocity, may also occur; these have no
net velocity and involve no net transfer
of energy.

Answer 4

WAVE

Question 5

is a substance made by
trapping air or gas bubbles inside a
solid or liquid. Examples are
formed by gases in liquids include sea
foams, fire retardant foam, and soap
bubbles. Rising bread dough may be
considered a semisolid. Solid
include dry wood, polystyrene
foam, memory foam, and mat foam

Answer 5

FOAM OR BUBBLES

Question 6

Is tiling that uses
shapes to cover a surface with no
gaps or overlaps. Picture a kitchen
floor with tiles.. This particular kitchen
floor is made up of all
squares. But, they aren’t
limited to just squares. They can be
any shape or any combination

Answer 6

Tessellations (Tiling)

Question 7

Occurs when the applied
stress is sufficient to break the atomic
bonds of the solid

Answer 7

Fractures

Question 8

propagation may be described
using the energy criterion theory
(Griffith, 1920) which is based on
thermodynamic and energy balance.

Answer 8

CRACKS

Question 9

Are made by series of bands or
strips, often of the same width and
color along the length. Nature’s love of
stripes and spots extends into the
animal kingdom like tigers and
leopards, zebras and giraffes.

Answer 9

STRIPES

Question 10

Is a never-ending pattern.
They are infinitely complex patterns
that are self-similar across different
scales. They are created by repeating
a simple process over and over in an
on-going feedback loop. For example:
trees, rivers, broccoli, cauliflower, blood
vessels and snowflakes.

Answer 10

FRACTALS

Question 11

It is a linear mapping method that
preserves points, straight lines, and
planes. The processes involved in affine
transformations are rotation, reflection
and scaling. Examples are broccolis
and cauliflowers.

Answer 11

AFFINE TRANSFORMATIONS

Question 12

is the series of numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …
The next number is found by adding up the two numbers before it:
 the 2 is found by adding the two numbers before it (1+1),
 the 3 is found by adding the two numbers before it (1+2),
 the 5 is (2+3),
 and so on!
When we make squares with those widths, we

Answer 12

FIBONACCI SEQUENCE

Question 13

came up with the sequence when calculating the ideal expansion pairs of
rabbits over the course of one year.

Answer 13

LEONARDO FIBONACCI

Answer 14

Conventions on Writing Sets