MATHEMATICS IN MODERN WORLD

PRELIM

PATTERNS IN NATURE

visible regular forms found in the natural world.

FRACTALS

infinitely self-similar, iterated mathematical constructs

SPIRALS

farther away on a point,

TESSELLATIONS

repeating tiles all over a flat surface.

BUBBLE/FOAMS

SPHERE WITH MINIMAL AREA

STRIPES

increase the chances that the offspring of the patterned animal will survive to reproduce.

CRACKS

linear openings that form in materials to relieve stress.

FIBONACCI SEQUENCE

characterized by each term being the sum of the two preceding terms?

ARITHMETIC SEQUENCE

a constant difference between consecutive terms

RADIAL SYMMETRY

symmetry do Plants possess

PRECISE

MAKE VERY FINE DISTINCTIONS

CONCISE

SAY THINGS BRIEFLY

POWERFUL

EXPRESS COMPLEX THOUGHT WITH RELATIVE EASE

EXPRESSION

represent a mathematical object of interest.

SENTENCE

states a complete thought.

RELATION

set of ordered pairs.

FUNCTION

ordered pairs is associated with exactly one value from the set of second

SET

collection of distinct well-defined objects

BRACKETS

show the correct notation in a set

Inductive

Generalized decision for observing witnessing specific instances of something (Specific to General)

Deductive reasoning

Taking info gather from general observe making specific decision based on info (General to Specific)

PROOF

to make each other believe our theorems. It's argument that convinces

GEORGE POLYA

Mathematician who created the famous four step problem solving strategy?

UNDERSTAND THE PROBLEM

• Identify what is being asked.

• Determine the known (given) information and the unknown (what you need to find).

• Restate the problem in your own words.

• Make sure you really understand it before moving on.

DEVISE A PLAN

• Think of possible strategies (e.g., drawing a diagram, making a table, looking for patterns, working backward, using equations).

• Choose the best method to approach the problem.

CARRY OUT THE PLAN

• Implement the chosen strategy step by step.

• Be careful and systematic with calculations.

• If the plan doesn’t work, don’t give up—try another approach.

LOOK BACK

• Check if your answer makes sense.

• Verify your solution by substituting it back into the problem.

• Think about what you learned—could there be a shorter or better method?