Mathematics in the Modern World: Midterm Review Notes

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What are patterns?

regular, repeated or recurring forms or designs.

How do patterns help us?

It helps us identify relationships and find local connections to form generalizations and make predictions.

What is symmetry?

An imaginary line across an object and the resulting parts are mirror images of each other.

What is symmetrical?

It is when an object remains the SAME or remains unchanged after a transformation.

What is bilateral symmetry?

It is when something is cut in half that the two portions are exactly the same.

What does Leonardo d Vinci’s Vitruvian Man show?

It illustrates the proportion and symmetry of the human body.

Leonardo da Vinci's Vitruvian Man google wise?

It is a drawing wherein leonardo combined art,math, and anatomy of a human. It was a big deal because leonardo was the first one to merge the circle and square perfectly as depicted in the drawing when a man stretches his arms out horizontally and stands with his feet together it forms a perfect square. It also depicts that if a man arms and legs are spread outwards and you put a measuring device at its navel his toes and fingers will touch the circumference.

What is rotational symmetry?

When an object or shape can be rotated around a central point and still look exactly as it did before it was turned.

Angle of Rotation

The measure of how much a figure turns around a fixed point called the center of rotation.

Order of rotation

Rotational symmetry of order n (The reason is that more area will be covered)

Honeycomb

Made by bees in hexagon (The reason is that more area will be covered)

Allan Turing

British mathematician that came up with the reaction-diffusion equations.

What is the reaction-diffusion eqations?

A system that governed the formation of hyena’s and tiger stripes.

What is Golden ratio?

Geometrically visualized as a rectangle perfectly formed by a square and another rectangle which can be repeated infinitely inside each section.

What is Physical beauty?

The proportions of the length of the nose, the position of the eyes and the length of the chin all conform to some aspect of the golden ratio.

what is the greek ratio of beauty Phi?

secret formula of perfection

What is Aesthetically pleasing?

Shapes and figures that bear the golden ratio.

What is Fibonacci sequence?

It is a series of numbers where each number is the sum of the two preceding ones.

Whos is the fibonacci man?

Leonardo Pisano Bogollo, He lived between 1170and 1250 in italy

What was Leonardo Pisano Boggolo’s nickname? & What does it mean?

Fibonacci was his nickname and it roughly means “Son of bonacci”

What is Arithmetic sequence?

The difference between one term and the next is a constant.

What is geometric sequence?

Each term is found by multiplying the previous term by a constant.

What is language?

A systematic means of communicating ideas or feelings by the use of conventionalized signs, sound, gestures, or marks having understood meanings.

What is Mathematics as language?

A system of communication about objects like numbers, variables, sets, operations, functions, and equations.

What are the importance of Language?

• It was invented to communicate ideas to others

• The language of mathematics was designed:

• Numbers

• Sets

• Functions

  • Perform operations

What is the grammar of mathematics?

Mathematical notation used for formulas has its own grammar, not dependent on a specific natural language, but shared internationally by mathematicians regardless of their mother tongues.

What are the characteristics of the mathematics language?

Precise, concise, and powerful

Precise meaning?

being able to make very fine distinctions.

Concise meaning?

being able to say things breifly.

Powerful meaning?

Being able to express complex thoughts with relative ease.

What could the word is mean?

It could mean equality, inequality, or members in a set.

Different use of numbers, such as?

Cardinal, ordinal, nominal, and ratio

Mathematical objects cane be represented in many ways such as?

Sets and functions.

Does the words “and” & “or” mean differently in mathematics from its english use.

yes

What is a variable?

It is a value represented by a letter, like y or x.

• Temporary name to what you were seeking so that you can perform a concrete computations with it to help discover its possible values.

What is mathematical language?

• The system used to communicate mathematical ideas.

• This language consists of some natural language using technical terms (Mathematical terms) and grammatical conventions that are uncommon to mathematical discourse, supplemented by a highly specialized symbolic notation for mathematical formulas.

• The mathematical notation used for formulas has its own grammar and shared by mathematicians anywhere in the globe.

What is the language of sets?

Math with things.

What is set?

collection of objects

What are elements?

Objects contained in a set.

What is Roster Method?

A particular set by listing its elements, separated by commas, within curly braces.

What is set builder notation?

A way of defining a set by describing its elements rather than listing them.

What is naming of sets?

It is conventional to use capital letters for names of sets.

What is cardinality?

The number of elements contained in the set.

What is equality of sets?

Two sets are equal if they have precisely the same members.

What are subsets?

It is from when we define a set, if we take pieces of that set.