Mathematics is something not everyone is good at, but it is something that is essential in our everyday life. Mathematics is not just about solving problems on paper but using theories in real-life scenarios.

There are various branches and sub-branches of mathematics. Two of them include Arithmetic and Geometry.ย

**Arithmetic vs Geometry**

**The main difference between Arithmetic and Geometry is that arithmetic involves linear variation, and geometry involves exponential variation. They are the two most important branches of modern mathematics. There are other differences between the two in terms of their earliest operational recordings, definitions, successive terms, finding of new terms, and utilizations.**

Arithmetic refers to a subdivision of mathematics consisting of number studies, including basic addition and subtraction. Number theory is among the top-level decisions of modern-day mathematics.

The others include geometry, algebra, and analysis. And an elementary part of this number theory is Arithmetic.

Geometry refers to another branch or subdivision of mathematics associated with the study of sizes, shapes, positions, angles, and the dimensions of different objects. Geometer is an individual working in the field of geometry.

Geometry can be traced back to the 2nd millennium BC in ancient Egypt and Mesopotamia.

**Comparison Table Between Arithmetic and Geometry**

Parameters of Comparison | Arithmetic | Geometry |

Meaning | A list of numbers or sequences in which each new number and the preceding number has a constant difference. | A list of numbers or sequences in which each new number and the preceding number has a constant ratio or multiple. |

Successive terms | There is a common difference between the two numbers. | There is a common ratio between the two numbers. |

New term | In sequence, the new term can be obtained by addition or subtraction. | In sequence, the new term can be obtained by multiplication or division. |

Variation | There is a linear variation of terms. | There is an exponential variation of terms. |

Sequence Example | 0, 3, 6, 9, 12, 15 | 3, 9, 27, 81, 6561 |

Utilization | It is a simple manipulation of numbers useful in everyday life. | It is related to properties of space associated with distance, shape, size, and relative position of objects or figures. It is useful in construction projects. |

**What is Arithmetic?**

Arithmetic refers to a subdivision of mathematics consisting of number studies, including basic addition and subtraction. Number theory is among the top-level decisions of modern-day mathematics.

The others include geometry, algebra, and analysis. And an elementary part of this number theory is Arithmetic. Until the 20th century, number theory and arithmetic were considered to be synonyms.

There are certain objects that showcase addition and subtraction is used, which go back to 20000 BC.

However, according to the proof, it can be stated that many of the elementary mathematical operations were used by Egyptians and Babylonians in 2000 BC. The historical development in the field, later on, took place in Ancient Greece.

Addition, Subtraction, Multiple, and Division are the basic operations of arithmetics. The advanced ones include square and square roots, percentages, exponentials, and logarithms.

The most common symbols are โ+โ for addition, โ-โ for subtraction, โxโ for multiplication, and โรทโ or โ/โ for division. Arithmetics involves a linear variation of terms.

In the Arithmetic sequence, the new term can be obtained by addition or subtraction. Arithmetics can be considered as the base of mathematics. It is also a very integral part of our daily activities.

**What is Geometry?**

Geometry refers to another branch or subdivision of mathematics associated with the study of sizes, shapes, positions, angles, and dimensions of different objects. Geometer is an individual working in the field of geometry.

Geometry can be traced back to the 2nd millennium BC in ancient Egypt and Mesopotamia.

Geometry at these early stages consisted of principles relating to lengths, angles, areas, and volumes. These principles were developed for the requirement of practical knowledge for the purpose of construction, crafts, astronomy, and surveys.

Egyptian Rhind Papyrus, Moscow Papyrus, and Babylonian clay tablets are some of the earliest recognized texts on geometry.

In terms of shapes and figures, geometry can be based on two types of objects 2D and 3D. Flat geometry is the study of 2D objects.

These objects have only 2 dimensions that include circles, triangles, squares, and rectangles. Solid objects or 3D objects are objects which have height as well as depth. This adds another dimension.

These objects include spheres, cones, cubes, and cuboids. In geometry, angles are of crucial importance. An angle is a vertex formed by any two rays or sides. In every arithmetic sequence, there is a common ratio. Geometry involves exponential variation.

**Main Differences Between Arithmetic and Geometry**

- Arithmetic relates to a list of numbers or sequences in which each new number and the preceding number have a constant difference. Geometry relates to a list of numbers or sequences in which each new number and the preceding number have a constant ratio or multiple.
- There is a common difference between two numbers in the Arithmetic sequence. There is a common ratio between two numbers in Geometry.
- ย In the Arithmetic sequence, the new term can be obtained by addition or subtraction. In Geometric sequence, the new term can be obtained by multiplication or division.
- There is a linear variation of terms in Arithmetics. There is an exponential variation of terms in Geometry.
- Example of Arithmetic sequence- 0, 3, 6, 9, 12, 15. Example of Geometric sequence- 3, 9, 27, 81, 6561
- Arithmetics is a simple manipulation of numbers useful in everyday life. Geometry is related to the properties of space associated with distance, shape, size, and relative position of objects or figures. It is useful in construction projects.

**Conclusion**

Arithmetic and Geometry are two branches of mathematics that are important. In the Arithmetic sequence, there is a common difference between two numbers. In Geometric sequence, there is a common ratio between two numbers.

In the Arithmetic sequence, the new term can be obtained by addition or subtraction. In Geometric sequence, the new term can be obtained by multiplication or division.ย

In arithmetics, thereโs linear variation, whereas, in geometry, thereโs exponential variation. Arithmetic mostly forms the base of mathematics, whereas geometry can seem like an advanced or complex version.

Arithmetic and Geometry may seem like they are the same concepts, but they are quite different from each other. They are two individual concepts helpful for individual purposes.

**References**

- https://link.springer.com/article/10.1007/BF00367686
- https://books.google.com/books?hl=en&lr=&id=PgHjLgIVidgC&oi=fnd&pg=PR13&dq=arithmetic+and+geometry+mathematics&ots=HsbtfxW4Dx&sig=q3df3gYh3j-7nuppRRj3VWOLL-k

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