Geometry and Algebra in Calculus

Running head: GEOMETRY AND ALGEBRA IN CALCULUS
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Geometry and Algebra in Calculus
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GEOMETRY AND ALGEBRA IN CALCULUS
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Introduction
Geometry is a mathematical branch that deals with properties and how they are related to lines,
surfaces, and solids. Mostly geometry deals with measurements and how points, angles or lines
relate to one another (Mirriam-Webster, 2019). Algebra is more of a representation, where
letters are used to represent or symbolizes numbers (Russell, 2018). We want to see how
algebra is brought about by geometry and how the two are used in calculus. In geometry, starts
from one dimensional figure, which have only dots, these are not usually measurable. From dots,
to another one-dimensional figures called lines, which is one point connected to the next point,
or dot, it has no thickness and extends infinitely in both directions, whether perpendicularly,
vertically, or diagonally.
How Geometry and Algebra Relates to Calculus
Geometry deals with lines, which is one dimensional, areas, which are two dimensional, and
volumes which are three dimensional. In one dimensional diagram, there’s only the length aspect
of it, two dimensional there’s the length and the width, in three dimensions, we have the area and
now the third dimension which is the thickness or height, this gives us the volume. Geometry
gives us the dimensions of all these.
To find the relationship of the areas, volume and the lengths of objects, they can be expressed
algebraically, like the length of an item can be l, the width can be expressed as w, and the height
expressed as h. These when put together gives representation of areas and volume
Area of a rectangle=l X w
The example above shows that to find an area you have to consider the length and width, which
are the two dimensions.
Area of a ̊¿ π r2
On this the representation is the radius of the circle and a constant π.
One thing we see from all of these is how the algebra relates to geometry.
So, if we find how geometry relates to calculus, then we shall have met what our research
proposes.
Calculus
Mostly this studies how things change, where there are instantaneous rates, and accumulation of
quantities in other words, differentiation and integration respectively. These are the two major
branches of calculus and they are connected by the basic theories of calculus. Calculus can be
applied in the calculation of an area. Especially when the regular shapes are plotted on a
cartesian plane or the irregular shapes.
When looking at the rate of change of dimensions, then we are talking about how the length
changes and the width. Yet on the other hand, when we talk about the geometric algebra in
relation to calculus, we are drawn to the basic equation of the differentiation;