Self-Similarity in Geometry, Algebra and Arithmetic
Subject: connection between algebra and geometry What are the today use algebraic manipulation, such as starting with a similarity. Algebraic geometry, the use of abstract algebra in geometry. 8. 4. Algebra is the study of relations, while calculus is the study of change. A variety of interesting examples of self-similar objects in geometry, arXiv admin note: substantial text overlap with arXiv:math/
The study of shape, size, relative position of figures, and the properties of space is one of immense historical importance for instance, how to know the value of a crop of olives?
Moreover, Geometry connects directly with our sense of vision and we can probably agree that we are highly visual creatures. Hence, Geometry provides a fertile soil for algebraic exploration and vice versa. In short, we would like to connect Algebra with Geometry and thereby providing a more solid understanding of both subjects. An interplay exists between algebra and geometry: Various authors have explained the connections between Algebra and Geometry in different ways.
Difference Between Algebra and Calculus
Other authors phrase this slightly different, for example one could say that connecting Algebra with Geometry means "Representing geometric situations algebraically and algebraic situations geometrically; using connections in solving problems". In any case we can probably agree that Geometry can serve as a model for Algebraic identities and thereby providing content and meaning to them.
This is a rather effective way to make sense in teaching Algebra and mathematics in general. Examples A few relevant examples are: Area Formulas Algebraic proofs of geometric theorems Geometric proofs of algebraic theorems Graphing Geometric representation of an expression Ratios, rates, scale measurements and similar drawings As usual, these are just a few out of many possible ways to connect Algebra with Geometry.
Let us take a closer look at the following examples: Equation of a circle This is a nice example of connecting Algebra with Geometry.
The only previous knowledge needed to construct an equation of a circle is that of distance between points. Area of a Triangle From the Geometric properties of area we know that the area of a rectangle or a parallelogram in general is just its base times its height.
Abstract algebra or modern algebra, wherein algebraic structures like groups, rings, and fields, are defined and investigated.
- Mathematics > Number Theory
Universal algebra, the study of common properties in algebraic structures. Linear algebra, the study of the properties of vector spaces and matrices.
Equations and geometry
Algebraic number theory, the study of the properties of numbers. Algebraic systems, the study of the theory of abstraction in algebra. Algebraic geometry, the use of abstract algebra in geometry. Algebraic combinatorics, the use of abstract algebraic methods to study combinatorial questions.
Similarity | Geometry (all content) | Math | Khan Academy
Calculus Calculus is a branch of mathematics that studies change. It is used to solve mathematical problems that cannot be solved by algebra and helps in determining the rate a variable will change in relation to others. Calculus has two major branches, differential and integral. Algebra is used in everyday life, while calculus is used in more complicated problems in professional fields like business, engineering, and science.
Algebra is an old branch of mathematics, while calculus is new and modern. Algebra is easier to understand, while calculus is very complex.