Podcast
Questions and Answers
It is a body of
knowledge and practice
It is a body of knowledge and practice
Mathematics
It was derived fromthe
contributions of
thinkers throughout the
ages and across the
globe
It was derived fromthe contributions of thinkers throughout the ages and across the globe
Mathematics
It gives us a way to
understand patterns, to
quantify relationships,
and to predict the future
It gives us a way to understand patterns, to quantify relationships, and to predict the future
Mathematics
Math helps us
understand the world —and we use the world to
understand math.
Math helps us understand the world —and we use the world to understand math.
Signup and view all the answers
Use of mathematics to model
situations or events in the
world;
Use of mathematics to model situations or events in the world;
Signup and view all the answers
Explanations of how the
complexity and
interrelatedness of situations or
events in the world are
reflected in the model;
Explanations of how the complexity and interrelatedness of situations or events in the world are reflected in the model;
Signup and view all the answers
Data generated by the
model to make and
defend a decision; and
Data generated by the model to make and defend a decision; and
Signup and view all the answers
A decision or
conclusion supported
by the mathematics
within the context of a
global community.
A decision or conclusion supported by the mathematics within the context of a global community.
Signup and view all the answers
The application of
appropriate strategies
to solve problems;
The application of appropriate strategies to solve problems;
Signup and view all the answers
The use of appropriate
mathematical tools,
procedures, and
representations to
solve the problem;
The use of appropriate mathematical tools, procedures, and representations to solve the problem;
Signup and view all the answers
The review and
proof of a correct
and reasonable
mathematical
solution given the
context.
The review and proof of a correct and reasonable mathematical solution given the context.
Signup and view all the answers
The development,
explanation, and
justification of
mathematical
arguments, including
concepts and
procedures used
The development, explanation, and justification of mathematical arguments, including concepts and procedures used
Signup and view all the answers
Coherently and clear communication using correct mathematical language and visual representations;
Coherently and clear communication using correct mathematical language and visual representations;
Signup and view all the answers
The expression of mathematical ideas using the symbols and conventions of mathematics.
The expression of mathematical ideas using the symbols and conventions of mathematics.
Signup and view all the answers
Patterns in nature are visible regular forms found in the natural world. The patterns can sometimes be modeled mathematically and they include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes.
Patterns in nature are visible regular forms found in the natural world. The patterns can sometimes be modeled mathematically and they include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes.
Signup and view all the answers
In 1202,Introduced the Fibonacci
number sequence. It turns out
that simple equations involving
the Fibonacci numbers can
describe most of the complex
spiral growth patterns found in
nature.
In 1202,Introduced the Fibonacci number sequence. It turns out that simple equations involving the Fibonacci numbers can describe most of the complex spiral growth patterns found in nature.
Signup and view all the answers
Belgian physicist Joseph Plateau
(1801–1883) formulated the
mathematical problem of the existence
of a minimal surface with a given
boundary, which is now named after
him. He studied soap films intensively
and formulated Plateau’s laws, which
describe the structures formed by films
in foams.
Belgian physicist Joseph Plateau (1801–1883) formulated the mathematical problem of the existence of a minimal surface with a given boundary, which is now named after him. He studied soap films intensively and formulated Plateau’s laws, which describe the structures formed by films in foams.
Signup and view all the answers
The German psychologist (1810–1876)
claimed that the golden ratio was
expressed in the arrangement of plant
parts, in the skeletons of animals and
the branching patterns of their veins
and nerves, as well as in the geometry
of crystals.
The German psychologist (1810–1876) claimed that the golden ratio was expressed in the arrangement of plant parts, in the skeletons of animals and the branching patterns of their veins and nerves, as well as in the geometry of crystals.
Signup and view all the answers
painted beautiful
illustrations of marine organisms,
in particular Radiolaria,
emphasizing their symmetry to
support his faux-Darwinian
theories of evolution.
painted beautiful illustrations of marine organisms, in particular Radiolaria, emphasizing their symmetry to support his faux-Darwinian theories of evolution.
Signup and view all the answers
The American photographer
Wilson Bentley (1865–1931) took
the first micrograph of a
snowflake in 1885.
The American photographer Wilson Bentley (1865–1931) took the first micrograph of a snowflake in 1885.
Signup and view all the answers
pioneered the
study of growth and formin his
1917 book.
pioneered the study of growth and formin his 1917 book.
Signup and view all the answers
better known for his
work on computing and
codebreaking, wrote The Chemical
Basis of Morphogenesis, an
analysis of the mechanisms that
would be needed to create
patterns in living organisms, in the
process called morphogenesis
better known for his work on computing and codebreaking, wrote The Chemical Basis of Morphogenesis, an analysis of the mechanisms that would be needed to create patterns in living organisms, in the process called morphogenesis
Signup and view all the answers
developed the L-system, a
formal grammar which can be used to model
plant growth patterns in the style of fractals. L-systems have an alphabet of symbols that
can be combined using production rules to
build larger strings of symbols, and a
mechanism for translating the generated
strings into geometric structures
developed the L-system, a formal grammar which can be used to model plant growth patterns in the style of fractals. L-systems have an alphabet of symbols that can be combined using production rules to build larger strings of symbols, and a mechanism for translating the generated strings into geometric structures
Signup and view all the answers
Symmetry is pervasive in living things. Animals
mainly have bilateral or mirror symmetry, as do
the leaves of plants and some flowers such as
orchids. • Plants often have radial or rotational symmetry,
as do many flowers and some groups of
animals such as sea anemones. • Rotational symmetry is also found at different
scales among non-living things including the
crown-shaped splash pattern formed when a
drop falls into a pond, and both the spheroidal
shape and rings of a planet like Saturn.
Symmetry is pervasive in living things. Animals mainly have bilateral or mirror symmetry, as do the leaves of plants and some flowers such as orchids. • Plants often have radial or rotational symmetry, as do many flowers and some groups of animals such as sea anemones. • Rotational symmetry is also found at different scales among non-living things including the crown-shaped splash pattern formed when a drop falls into a pond, and both the spheroidal shape and rings of a planet like Saturn.
Signup and view all the answers
are infinitely self-similar, iterated
mathematical constructs having fractal
dimension. Infinite iteration is not possible in
nature so all ‘fractal’ patterns are only
approximate.
are infinitely self-similar, iterated mathematical constructs having fractal dimension. Infinite iteration is not possible in nature so all ‘fractal’ patterns are only approximate.
Signup and view all the answers
are common in plants and in some
animals, notably molluscs.
are common in plants and in some animals, notably molluscs.
Signup and view all the answers
are sinuous bends in rivers or other
channels, which form as a fluid, most often
water, flows around bends. As soon as the path
is slightly curved, the size and curvature of
each loop increases as helical flow drags
material like sand and gravel across the river to
the inside of the bend. The outside of the loop
is left clean and unprotected, so erosion
accelerates, further increasing the meandering
in a powerful positive feedback loop.
are sinuous bends in rivers or other channels, which form as a fluid, most often water, flows around bends. As soon as the path is slightly curved, the size and curvature of each loop increases as helical flow drags material like sand and gravel across the river to the inside of the bend. The outside of the loop is left clean and unprotected, so erosion accelerates, further increasing the meandering in a powerful positive feedback loop.
Signup and view all the answers
are disturbances that carry energy as
they move. Mechanical waves propagate
through a medium – air or water, making it
oscillate as they pass by
are disturbances that carry energy as they move. Mechanical waves propagate through a medium – air or water, making it oscillate as they pass by
Signup and view all the answers
Dunes may form a range of patterns including
crescents, very long straight lines, stars,
domes, parabolas, and longitudinal or Seif
(‘sword’) shapes.
Dunes may form a range of patterns including crescents, very long straight lines, stars, domes, parabolas, and longitudinal or Seif (‘sword’) shapes.
Signup and view all the answers
A soap bubble forms a sphere, a surface with
minimal area — the smallest possible surface
area for the volume enclosed
A soap bubble forms a sphere, a surface with minimal area — the smallest possible surface area for the volume enclosed
Signup and view all the answers
are patterns formed by
repeating tiles all over a flat surface.
are patterns formed by repeating tiles all over a flat surface.
Signup and view all the answers
are linear openings that formin
materials to relieve stress.
are linear openings that formin materials to relieve stress.
Signup and view all the answers
Leopards and ladybirds are spotted;
angelfish and zebras are striped. • These patterns have an evolutionary
explanation: they have functions which
increase the chances that the offspring of
the patterned animal will survive to
reproduce. • One function of animal patterns is
camouflage; for instance, a leopard that is
harder to see catches more prey
Leopards and ladybirds are spotted; angelfish and zebras are striped. • These patterns have an evolutionary explanation: they have functions which increase the chances that the offspring of the patterned animal will survive to reproduce. • One function of animal patterns is camouflage; for instance, a leopard that is harder to see catches more prey
Signup and view all the answers
