Introduction to Mathematics

• Mathematics is derived from the Greek words "manthanein," meaning learning, and "techne," meaning an art of technique
• Math is the art of learning related disciplines
• Mathematics is the science of quantity, measurement, and special relations
• Mathematics deals with the logic of shape, quantity, and arrangement and is around us in everything
• It is the building block for day to day life, including mobile devices, architecture art, money, engineering, and even sports
• Mathematics provides opportunities to make independent discoveries
• Mathematics is the discovery of relationships and the expression of those relationships in symbolic form
• Mathematics is mainly a matter of puzzles, paradoxes, and problem-solving
• Mathematics has integrity, beauty, and structure
• Intuition is the first step in learning any mathematical subject, and must come before formal rules or operations
• Mathematical ideas are communicated largely with symbols and words which not everyone understands
• Mathematics is an abstract science because mathematical concepts cannot be seen or felt in the physical world
• Logic governs the pattern of deductive proof in mathematics
• Conclusions in mathematics are certain and definite, so learners can check for correct solutions
• Learning mathematics helps apply mathematical concepts and theorems to new situations and provides understanding of laws of nature
• Mathematics helps understand culture and civilization and helps to think of alternative methods of solving problems providing a framework for it

Mathematics in daily life

• Cooking involves measuring ingredients like tablespoons, ounces and grams
• Measurements can be disastrous if messed up
• Overweight people need to be conscious of their calorie intake, and thus need math to calculate the total amount of calories consumed in a day when dieting
• Banking uses math more than anywhere else, as it being impossible to do anything without the knowledge of math
• Artists use math when they're making paintings, designing collages, as well as during dance performances
• In all of the above cases, the size of canvas, the size of the stage, etc play a very important role in math
• To buy things, shopping requires math, when we make a list of things we need to buy as well payments
• Gardening whether is the planning of sowing seeds to counting of the numbers of plants, math is required
• All tasks carried out inside a garden require proper measurements

Patterns in nature

Natural patterns include symmetries, fractals, spirals, meanders, stripes, waves, foams, tessellations, and cracks

• Studying patterns allow one to watch, guess, create and discover.

Symmetry

• This is an exact correspondence of form and constituent configuration on the opposite sides of a dividing line or plane or about a center or and axis

Reflection or bilateral

• This is also called mirror or line symmetry
• It is when there is line going through an object that divides it into two pieces which are mirror images of each other

Radial symmetry

• This is rotational symmetry around a fixed point known as the center

Translational symmetry

• This is the kind of symmetry exhibited by objects which do not change its site and shape
• This is even if the item is moved to another location
• The movement does not involve with rotation nor reflection

Fractals

• Fractals are never-ending patterns that are self-similar across different scales
• The image reappears repeatedly no matter how many times the object is magnified

Spirals

• Spirals are curved patterns made by series of circular shapes revolving around a central point

Spots and stripes

• These are patterns also exhibited in the external appearances of animals

Flower petals

• Flowers are considered things of beauty due to their vibrant colors and fragrant odors, which make them very appealing as gifts and decorations

Number patterns and sequences

• Patterns in numbers exist

Mathematics is derived from the Greek words for 'learning' and 'art of technique'. It is the building block for day-to-day life and provides opportunities to make independent discoveries. Mathematics is the discovery of relationships in symbolic form, puzzles, paradoxes, and problem-solving.