math 2

65問 • 1年前

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Is a fundamental branch of knowledge that deals with the study of numbers, quantities, space, and patterns

mathematics

It is both a science and an art that involves the use of logical reasoning, abstraction, and critical thinking to solve problems and understand the relationships between mathematical concepts

mathematics

Is characterized by its abstract and logical nature

nature of mathematics

It deals with concepts and relationships that exist in the realm of the mind and can be expressed through symbols and formulas

mathematics

Provides a way to understand the patterns and structures that underly many natural phenomena and human activities

mathematics

Mathematics is a highly _____ field. Mathematical concepts can be studied and explored purely through thought experiments and logical reasoning.

abstract

Mathematical ideas and principles are ______, meaning that they apply to all cultures and societies, and are not dependent on specific context or circumstances.

universal

Mathematics is also highly ______ field, in which mathematicians explore and discover new ideas and connections between seemingly unrelated concepts.

creative

Despite its abstract and universal nature, mathematics also has many ______ applications and fields such as science, engineering, finance, and computer science.

practical

Are sequences of numbers that follow a certain rule or formula

number patterns

These patterns can appear in various forms and can be found in many areas of mathematics and science

number patterns

The arithmetic pattern is also known as

algebraic pattern

The algebraic pattern is also known as

arithmetic pattern

In this pattern, the sequences are based on the addition or subtraction of the terms

arithmetic patterns

Is defined as the sequence of numbers that are based on the multiplication and division operation

geometric pattern

Are a sequence of numbers that can be represented as series of dots or the sum of consecutive integers

triangular numbers

Is a series of numbers in which each number is the sum of the two preceding numbers

fibonacci sequence

The ______ is named after LEONARDO FIBONACCI an ITALIAN MATHEMATICIAN who introduced the sequence the Western world in his book "LIBER ABACI" in 1202

FIBONACCI SEQUENCE

The FIBONACCI SEQUENCE is named after _______ an ITALIAN MATHEMATICIAN who introduced the sequence the Western world in his book "LIBER ABACI" in 1202

LEONARDO FIBONACCI

The FIBONACCI SEQUENCE is named after LEONARDO FIBONACCI an ______ who introduced the sequence the Western world in his book "LIBER ABACI" in 1202

ITALIAN MATHEMATICIAN

The FIBONACCI SEQUENCE is named after LEONARDO FIBONACCI an ITALIAN MATHEMATICIAN who introduced the sequence the Western world in his book "_____" in _____

LIBER ABACI 1202

The spiral shells of snails and nautiluses are formed through a process called ______, it is a mathematical pattern that can be found in any natural and man-made systems

logarithmic spiral growth

The _____ of snails and nautiluses are one of the most iconic examples of patterns in nature

spiral shells

The logarithmic spiral is also known as

growth spiral equiangular spiral spira mirabilis

____ are defined by the equation r = ae ^ kφ

Logarithmic spirals

Logarithmic spirals are defined by the equation

r = ae ^ kφ

Logarithmic spiral r = ae ^ kφ r is the

distance from the center

Logarithmic spiral r = ae ^ kφ φ is the

angle of rotation

Logarithmic spiral r = ae ^ kφ k

contangent of the polar tangential angle

Logarithmic spiral r = ae ^ kφ a is a CONSTANT that determines the

scale of the spiral

This means that the distance between successive terms of the spiral increases by a constant factor as the spiral grows

logarithmic spirals

Logarithmic spirals is related to fibonacci numbers, the golden ratio, and the golden rectangle, and a sometimes called

golden spiral

______ discovered a formula for calculating any fibonacci number

Leonhard euler

The formula for calculating any fibonacci number was lost or about 100 years and was discovered by another mathematician named

jacques binet

Do the golden ratio is represented by the greek letter

phi

Is a mathematical constant and is defined as the ratio of two quantities such that the ratio of the sum of the two quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller quantity

golden ratio

It is an irrational number that keeps going like pi

golden ratio or phi

The actual value of golden ratio is

1.61803398874989

Describes the perfectly symmetrical relationship between two proportions

golden ratio

Approximately equal to a 1:1.61 ratio

golden ratio

The golden ratio can be illustrated using a

golden triangle

Refer to recurring recognizable structures or arrangements that can be observed in the natural world

patterns in nature

The _____ was first studied by DESCARTES in 1638 and JACOB BERNOULLI

LOGARITHMIC SPIRAL

The LOGARITHMIC SPIRAL was first studied by _____ in _____ and _____

DESCARTES 1638 JACOB BERNOULLI

Can be found when analyzing patterns of seeds on a sunflower

fibonacci sequence

The golden angle is approximately

137.5°

Are common natural phenomena that exhibit wave like behavior and can be described using mathematical models of wave mechanics

dunes and waves patterns

Are common in nature and can be found in a wide variety of animals, from big cats like tigers and leopards to insects like ladybugs and beetles

spots and stripes

A repeating patterns of shapes that completely cover a surface without any gaps or overlaps

tessellations

Hexagonal shapes of honeycomb to the geometric patterns on the shell of a circle

tessellations

Ocean waves are example of

dunes and waves patterns

Refers to a balanced and proportionate arrangement of elements or parts that are identical or mirror images of each other

symmetry

Are geometric shapes or patterns that repeat at different scales and our characterized by their self similarity

fractals

It is a mathematical object that looks similar at different levels of magnification

fractals

The term "_____" was coined by BENOIT MANDELBROT in the 1970s who defined it as a shape that exhibits "SELF SIMILARITY AT ALL SCALES"

FRACTAL

The term "FRACTAL" was coined by ______ in the ______ who defined it as a shape that exhibits "SELF SIMILARITY AT ALL SCALES"

BENOIT MANDELBROT 1970s

The term "FRACTAL" was coined by BENOIT MANDELBROT in the 1970s who defined it as a shape that exhibits "______"

SELF SIMILARITY AT ALL SCALES

Fractal shapes can be generated through a process called ______ where a simple geometric shape is repeated over and over again, each time with some variation or transformation

iteration

Is a set of complex numbers that exhibits a highly complex and intricate fractal pattern when plotted in the complex plane

mandelbrot set

Is a beautiful and fascinating pattern that illustrates the power of mathematical abstraction and the beauty and complexity of fractal patterns in nature

sierpinski triangle

______ is named after the polish mathematician WACLAW SIERPINSKI, who discovered it in 1915

SIERPINSKI TRIANGLE

SIERPINSKI TRIANGLE is named after the polish mathematician ______, who discovered it in ____

WACLAW SIERPINSKI 1915

This pattern is generated by a recursive process, in which an equilateral triangle is divided into four smaller equilateral triangles and the middle triangle is removed

Sierpinski triangle

Is a fractal pattern named after the swedish mathematician HELGE VON KOCH, first described it in 1904

Koch snowflake

Koch Snowflake is a fractal pattern named after the swedish mathematician _____, first described it in ____

HELGE VON KOCH 1904

Business Finance

Sab Sescon · 46問 · 2年前

Business Finance