Geometric figures may be drawn on paper for easy visualization. However, it is said to be the Math of space. How would you explain the space of Geometry?
Space around us is the physical space of the universe. It may have air or be without air or anything but it still remains the physical space. Space of Geometry, on the other hand, is an imaginative space that exists in our thinking.
Why are the negative numbers so important?
Negative numbers are less than zero. Zero is often understood to represent a nothing and the question may arise that how can anything be less than nothing. However, numbers whether positive or negative, are not things but ideas or abstractions. They may be used for counting things. The abstraction of negative numbers may seem rather unnatural. But all numbers, whether positive or negative, are mere ideas that are also of great use in the real world. Negative numbers may be thought of as enabling backward counting from zero. In addition to its use as representing nothing, a zero may also represent an origin or a neutral point or even any fixed point. As an example, if sea level is taken as zero then height above sea level is taken as positive while depth below sea surface is taken as negative height. Depositing money in a bank account increases bank balance and is taken as positive. Withdrawal of money is the opposite and is taken as negative.
Why are the variables so important to Algebra?
Algebra helps to know values of numbers that are not known. Such unknown numbers in algebra are represented by alphabets. These alphabets are called variables as they can hold more than one number values that are different from one another. This results naturally from solving quadratic or higher degree equations.