CARL FRIEDRICH GAUSS: A PHENOMENAL INVENTOR SINCE THE AGE OF 10

Oleh

Assyfa Razaqi¹, Azlin Fahira², Lelen Purnama Sari³, Nasywa Adila Rahma⁴

(Departement Of Mathemathics and Data Science, FMIPA, Andalas University, Indonesia.)

Carl Friedrich Gauss was a mathematician who changed the paradigm with his discovery in arithmetic series. Gauss' arithmetic sequence became an important foundation in the development of more complex mathematical concepts and has inspired generations of mathematicians to explore further in this field. Gauss' genius for recognizing mathematical patterns and his ability to quickly calculate the terms of a series became a lasting legacy in modern mathematics. Gauss' discoveries in arithmetic series not only influenced mathematics education, but also provided inspiration for further mathematical developments and research.

The article on Gauss as the inventor of the arithmetic series will be based on some relevant theoretical foundations. There are some theoretical concepts that can be used in the article:

1.     Arithmetic Series: The article can explain the basic concept of an arithmetic series, which is a sequence of numbers with a constant difference between each consecutive pair of numbers. The Gauss formula, also known as the arithmetic series sum formula, can be explained as a method to calculate the sum of a series.

2.     Gauss's discovery: The article may discuss the life and contributions of Carl Friedrich Gauss as a German mathematician in the 18th and 19th centuries.

3.     Application of Gauss' Formula: The article can explain the various applications of Gauss' formula in mathematics and related sciences. For example, the formula can be used to calculate the sum of integers from 1 to n, calculate the sum of terms in an arithmetic pattern, or calculate the number of elements in a regular sequence of numbers.

4.     The Importance of Arithmetic Series: The article can explain the importance of arithmetic series in math and related sciences. Arithmetic series are used in various fields, such as physics, economics, statistics, and computer science.

5.     Further Development of Mathematics: The article can discuss how Gauss' discovery of arithmetic series has encouraged further development of mathematics. For example, Gauss' formula became the basis for the development of the geometric series sum formula and the infinite series sum formula.

GAUSS BIOGRAPHY

Source: sapaviva.com

Johann Carl Friedrich Gauss was born on April 30, 1777, in Brunswick (Braunschweig), in the County of Brunswick-Wolfenbüttel (now part of Lower Saxony, Germany), into a family of lower-middle social status. His father, Gebhard Dietrich Gauss (1744–1808), worked at several jobs as a bricklayer, gardener, and treasurer of a death benefit fund. Gauss was a mathematical genius. While still a student at the University of Göttingen, he proposed several mathematical theorems. Gauss completed his best works, Disquisitiones Arithmeticae and Theoria motus corporum coelestium, as a private scholar. He later became director of the Göttingen Observatory and professor at the university for almost half a century, from 1807 until his death in 1855.

In addition to the arithmetic series, Gauss also contributes to the normal distribution curve. Gauss' contribution to probability theory is the Gaussian curve which is often referred to as Gauss' law, which is about the normal distribution or what is now better known as a bell-shaped curve. Errors will collect half on the left side and half on the right side of the curve. "Incidental" errors can be called incidents, according to Gauss, always occur with a frequency that can be predicted in advance according to mathematics. The larger the sample, the more accurate the prediction of errors that will occur. Scientists eventually discovered that not only errors in certain disciplines, but almost all phenomena follow this law.

This discovery is one of the greatest inventions of all time. It is almost impossible to count population data. Even if we could, it would be inefficient in time, cost, and energy. With Gauss's discovery, the population can be estimated with accuracy that can also be measured scientifically, with a portion of the population data taken randomly under special conditions. A graph representing the density function of a normal probability distribution is also known as the Normal Curve or Bell Curve.

One needs to specify two parameters, the mean and the standard deviation. In the graph it must have a mean of zero and a standard deviation of 1. A normal distribution with a mean of zero and a standard deviation of 1 is also known as the Standard Normal Distribution. The characteristics of a normal distribution include having the parameters µ and ? which determine the location and shape of the curve. The normal distribution is a symmetric distribution. The standard deviation determines the width of the curve. The total area of the curve is 1.

Source: wikiwand.com

There are several applications of the Gaus formula in various fields, namely:

1.     Mathematics: The Gauss formula is used to sum an arithmetic series or a geometric series. For example, to sum integers from 1 to 100, we can use the Gauss formula: where Sn is the sum of the series, n is the number of terms, a is the first term, and l is the last term.

2.     Statistics: The Gauss formula is used in the normal distribution, or Gauss distribution. The normal distribution is a probability distribution often used in statistical analysis. The Gauss formula is used to calculate the probability or z-score value in a normal distribution.

During his life, Gauss won the Copley Medal, Britain's most prestigious scientific award, given annually by the Royal Society of London, in 1838 "for his mathematical discoveries and research in magnetism". In 1823, the Danish Academy of Sciences presented him with an honor for his research on angle-preserving maps.

We cannot underestimate the importance of Gauss' discovery of the arithmetic series. This discovery has provided a strong foundation for the development of mathematics and its applications in various fields. Gauss is a shining example of intelligence and perseverance in exploring the world of mathematics and making tremendous contributions to mankind.

REFERENCES

The editor of Encyclopedia Britannica. What awards did Carl Friedrich Gauss Win?. Accessed on November 30th, 2023. https://www.britannica.com/question/What-awards-did-Carl-Friedrich-Gauss-win

Wight, Randal D & Gable, Philip A (2005). Gauss, Johan Carl Friedrich. Encyclopedia of statistics in Behavioral Science. Volume 2, pp. 694-696.

Akuindo (2023). Carl Friedrich Gauss. Wikipedia. https://id.wikipedia.org/wiki/Carl_Friedrich_Gauss

Pontes, Edel Alexandre Silva (2018). A Brief Historical Overview Of The Gaussian Curve: From Abraham De Moivre to Johann Carl Friedrich Gauss. International Journal of Engineering Science Invention. 4-6.