math

Mathematics of Our World

1. Mathematics is a tool 2. Mathematics is everywhere 3. Mathematical Landscape 4. The Essential Roles of Mathematics 5. How Mathematics is Done 6. Mathematics is for everyone

Types of Sequence

Arithmetic Geometric Harmonic Fibonacci

It is a sequence of numbers that follows a definite pattern. To determine if the series of numbers follow an arithmetic sequence, check the difference between two consecutive terms. If common difference is observed, then definitely arithmetic sequence governed the pattern.

Arithmetic Sequence

is a series of numbers governed by some unusual arithmetic rule. The sequence is organized in a way a number can be obtained by adding the two previous numbers. This specific sequence was named after an Italian mathematician Leonardo Pisano Bigollo (1170 - 1250) also known as Leonardo of Pisa. He discovered the sequence while he was studying rabbits.

Fibonacci Sequence

a sequence, where each term after the first is found by multiplying the preceding term by a constant "r'. Number "r" is called common ratio of geometric sequence. we need to look for the common ratio

GEOMETRIC SEQUENCE

is a kind of pattern which consists of a series of shapes that are typically repeated. These are regularities in the natural world that are repeated in a predictable manner. Geometrical patterns are usually visible on cacti and succulents.

Geometric Patterns

In the sequence, the reciprocal of the terms behaved in a manner like arithmetic sequence. Consider the example below and notice an interesting pattern in the series. With this pattern, the reciprocal appears like arithmetic sequence. Only in recognizing the appearance that we can finally decode the sequencing govern the series

Harmonic Sequence

is a structure, form, or design that is regular, consistent, or recurring. Patterns can be found in nature, in human-made designs, or in abstract ideas. They occur in different contexts and various forms.

PATTERNS

provides an inexhaustible supply of nature's patterns. Patterns of flow are usually found in the water, stone, and even in the growth of trees. There is also a flow pattern present in meandering rivers with the repetition of undulating lines.

Patterns of Flow

In the human walk, the feet strike the ground in a regular rhythm: the left-right- left-right-left rhythm. When a horse, a four-legged creature walks, there is more of a complex but equally rhythmic pattern. This prevalence of pattern in locomotion extends to the scuttling of insects, the flights of birds, the pulsations of jellyfish, and also the wave-like movements of fish, worms, and snakes.

Patterns of Movement

is conceivably the most basic pattern in nature. Our hearts and lungs follow a regular repeated pattern of sounds or movement whose timing is adapted to our body's needs. Many of nature's rhythms are most likely similar to a heartbeat, while others are like breathing. The beating of the heart, as well as breathing, have a default pattern.

Patterns of Rhythm

is a quality of a certain object that we sense through touch. It exists as a literal surface that we can feel, see, and imagine. Textures are of many kinds. It can be bristly, and rough, but it can also be smooth, cold, and hard.

Patterns of Texture

are often unpredictable, never quite repeatable, and often contain fractals. These patterns are can be seen from the seeds and pinecones to the branches and leaves. They are also visible in self-similar replication of trees, ferns, and plants throughout nature.

Patterns of Visuals

sometimes called line symmetry or mirror symmetry, captures symmetries when the left half of a pattern is the same as the right half.

Reflection symmetry

also known as rotational symmetry, captures symmetries when it still looks the same after some rotation (of less than one full turn). The degree of rotational symmetry of an object is recognized by the number of distinct orientations in which it looks the same for each rotation

Rotations

refers to an ordered list of numbers called terms, that may have repeated values. The arrangement of these terms is set by a definite rule.

Sequence

This is another type of symmetry. Translational symmetry exists in patterns that we see in nature and in man-made objects. Translations acquire symmetries when units are repeated and turn out having identical figures, like the bees' honeycomb with hexagonal tiles.

Translations

In mathematics, if a figure can be folded or divided into two with two halves which are the same, such figure is called has a vital role in pattern formation. It is used to classify and organize information about patterns by classifying the motion or deformation of both pattern structures and processes.

symmetry

DIFFERENT TYPES OF PATTERNS

• Patterns of Visuals • Patterns of Flow • Patterns of Movement • Patterns of Rhythm • Patterns of texture • Geometric Patterns