Exploring properties associated with numbers including their geometric representations

 

Exploring properties associated with numbers including their geometric representations

Arithmetic  is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication, division, exponentiation and extraction of roots.  Algebra is described as an area in mathematics that uses variables, in the forms of letters and symbols, to act as numbers or quantities in equations and formulas.  Geometry, on the other hand, is described as an area in mathematics that studies points, lines, varied-dimensional objects and shapes, surfaces, and solids.

Relationships Between Geometry, Arithmetic  and Algebra

As we said, algebra has to do with equations and formulas, and geometry has to do with objects and shapes, so how can these two things be related? Well, as one example, you are probably familiar with the fact that an equation can be graphed. For instance, the equation

y = x + 3 is the graph of a set of points that satisfy the equation, and it turns out to be a straight line.

 

We can take an equation, which is an algebraic concept, and graph it, making it a geometric concept.

In general, the equation of a line has the form y = mx + b, where m is equal to the slope of the line (where the slope is the change in y-values divided by the change in x-values from one point to the next on the line) and b is equal to the y-intercept of the line. We see that the variables within the equation (both algebraic concepts) can actually be used to refer to geometric concepts (slope and y-intercept) of the line.

 

Consider the shapes of a circle, rectangle, and square. These shapes fall under the category of a geometric concept. However, what about the areas of these shapes? To find the areas of each of these shapes, we use algebraic formulas and use the numbers to find the final value.

Pythagorean Theorem:

 It's a theorem that states that if a right triangle has legs of lengths a and b, and a hypotenuse of length c, then a² + b² = c².

The theorem itself shows a relationship between geometry and algebra by relating the lengths of the sides of a right triangle (a geometric concept) to an equation (an algebraic concept).

Relationships  between Geometry & Arithmetic:  

Geometry, an important branch of Mathematics, has a place in education for the development  of critical thinking and problem solving, furthermore, that geometrical shapes are parts of our  lives as they appear almost everywhere, geometry is utilized in science and art as well. Using the concept of  Geometry and their shapes we can teach Arithmetic in a  better way. Suppose we are going to teach addition and subtraction, we may use the line concept or shape of any objects. When we are going to teach Integers we may apply draw the line & explain it. If we are going to teach fraction we may use circle shapes. We divide circle in different part and give the concept of different types of fraction ,  If we are going to teach Arithmetic progression we may apply the rectangles shapes like stairs,  etc.

 

 

Concept of   Integers:

 

 

 

 

          

 

   Concept of   Tn terms of Arithmetic progression: