Jahelly Maxwell: Italia America 2022

The Influence of Ancient Rome on Modern Mathematics

by: Jahelly Maxwell

MATH DURING THE RENAISSANCE

The Renaissance was a period of time between the 14th and 17th century where art, literature, and science evolved. It came after the Medieval times and is said to be the bridge between the Middle Ages and Modern history.

Geometry and mathematics were important in all areas, such as architecture, paintings, and trade. Many people of the Renaissance introduced and/or created tools to help advance math to what it is today.  Mathematics from Ancient Rome, with its mix of science and breathtaking architecture, brought about many worldly advances which include most of the mechanisms we use in our everyday math.

ROOTS

Roman mathematics was originally derived from Greek mathematics, and was heavily influenced by knowledge from the Ancient Greeks. The Roman Empire was one of the world’s most extensive territorial and innovative empires in history. The Romans ruled over most of Europe and were ruthless conquerors.  They had the Greek and Hellenistic empires by the middle of the 1st Century B.C.  Upon being heeded by the Roman empire, the Greeks’ mathematical revolution had come to an end.

All images are in the public domain.

ROMAN NUMERALS

Roman numerals originated in ancient Rome, between 900 and 800 B.C., as their name suggests. They quickly became the most common way of writing numbers throughout the rest of Europe well into the late Middle Ages. Roman numerals began as a collection of seven fundamental numerical symbols.

Those symbols evolved into the letters we use today as time. The numeric system used in ancient Rome makes use of combinations of letters from the Latin alphabet to indicate values. In Roman numerals, the numbers 1 to 10 can be denoted as follows:

I, II, III, IV, V, VI, VII, VIII, IX, X.

Roman numerals function through a process called Subtractive Notation. The system is broken down into a basic method of comparing the numbers from left to right. If there is a larger number on the left, or the both numbers are the same, the procedure would be to add. If the smaller number is towards the left side, one would subtract it from the larger number on the right. 
Hence, II is 1 +1 = 2 for addition, and IV is 5 – 1 = 4.

Roman numerals are everywhere. It is quite shocking how frequently the symbols appear once one is familiar with them and how they’re used.  They are often used in books to number the chapters, in plays to separate acts into sections, and in appendices or introductions much like that of the United States’ Constitution. Roman numerals can also be seen on fancy clocks, hand watches, and sometimes even in family names.  Many generations have inherited a family name that incorporates a Roman numeral to identify a family member. If a man’s name is John Smith and his father and grandparents were both named John, he would be known as John Smith III. This approach is often used by royal families.

THE IMPORTANCE OF MATHEMATICS

Math is essential because we utilize it intrinsically  on a daily basis. It may be quite useful in both our personal and professional lives. Most classes taught nationwide in the United States from grades K-12 involve some form of mathematics. Some courses are soft sciences which include Economics, Psychology, and Sociology and hard sciences like Biology, Chemistry Physics, and Engineering fields, such as civil, mechanical, and industrial engineering. Arts (sculpture, drawing, and music) also include mathematics to an extent. Some careers paths and activities practiced within the United States in which math can be used are:

Accountants aid businesses by assisting them with their taxes and planning for the future. They work with tax laws and documents, calculate interest using formulas, and spend a significant amount of time organizing paperwork.

Agriculturists figure out how much fertilizer, insecticides, and water to use to generate a plentiful harvest. They must be familiar with chemistry and difficulties involving mixtures.

Architects create structures that are both stable and visually pleasing. They must be able to calculate loads in order to locate appropriate materials in design, which demands a knowledge of calculus.

Biologists study nature because we are so intertwined with it and to make statistical assumptions they use proportions which is a topic usually found within statistics/probability. 

Chemists discover new ways to employ chemicals (involving meticulous mathematical calculations) to help us, such as purifying water, managing trash, investigating superconductors, analyzing crime scenes, creating food items, collaborating with biologists to explore the human body, and so on.

Cooks follow recipes that use math. Basic arithmetic is used to figure out how many ingredients you’ll need for the dish, and so on. When doubling or halving a recipe, fractions for addition, subtraction, multiplication, and division are utilized. Math essentially also calculates how much food will be needed to make based on the amount of people who are eating. 

Computer Programmers write complex programs on computer softwares that assist with solving problems. They must be logical, critical thinkers, and problem solvers.

Engineers (Chemical, Civil, Electrical, Environmental Industrial, Material, Mechanical, etc.) build and create tangible products, edifices and structures, mechanisms like automobiles, computers, electrical machines, and airplanes. They can’t avoid using a variation of calculus on a regular basis.

All images are in the public domain.

Lawyers use complicated lines of reason to argue for their cases. This precise skill is nurtured by high level mathematics. Lawyers also spend a considerable amount of time researching and referring to cases, which implies learning, perhaps sometimes memorizing the numbered relevant laws, codes and ordinances. Building cases requires a strong sense of numerical notation .

Managers construct complex schedules, statistically regulate worker performance, and mathematically analyze productivity.

Meteorologists forecast the weather for agriculturists, pilots, vacationers, and people who rely on the sea for transportation. They interpret intricate mapping schemas, and heavily work with computer modeling platforms which to an extent require a fundamental understanding of the mathematical laws of physics.

Military personnel are responsible for a wide range of responsibilities, including aircraft maintenance and following rigorous protocols. Linear programming is a field of mathematics that tacticians use.

Nurses adhere to the doctors’ specific instructions. They control the rate of painkilling drugs, assess physiological data, and even help with procedures.

Politicians contribute to the settlement of today’s societal problems by making difficult decisions within the bounds of the law, public opinion, and (ideally) budgetary constraints.

Salespeople are usually paid on commission and follow a ‘buy cheap, sell high’ profit strategy. Their work involves excellent interpersonal skills as well as the ability to estimate fundamental math problems without using paper or pencil.

Technicians fix and maintain the devices we rely on, such as computers, televisions, DVD players, automobiles, refrigerators, and so on. They are constantly reading measuring instruments, consulting manuals, and diagnosing system issues.

Tradesmen (carpenters, electricians, mechanics, and plumbers) assess job expenses and apply specialized math abilities to their work. They work with areas, volumes, slopes and distances, hence needing a strong mathematical background.

NOTABLE ITALIAN MATHEMATICIANS

Mathematical contributions have been part of the building blocks for future generations for as long as documentation has existed. The following mathematicians are all intrinsically studied up until Calculus III in the United States. It is likely they are studied in any higher level mathematics as well, they are just encompassed heavily in schooling systems across the nation throughout these calculus courses: I, II, and III.

Archimedes, Fibonacci, Lagrange

ARCHIMEDES (287BC – 212BC) 

Archimedes was born in the seaport city of Syracuse on the island of Sicily in 287 BC. He was a well respected Italian/Grecian mathematician, inventor, engineer, and scientist. Among his developments and advances of principles in calculus, Archimedes is universally considered to be one of the greatest mathematicians of all time. So much so, he is distinguished as the Father of Mathematics. He was the first to discover integral calculus,  2000 years before Newton.  Some of Archimedes’ contributions in calculus include:

Measurement of the Circle
The approximation of π (pi) is one of Archimedes’ most renowned works, in which he estimated the exact value of π to be between 3 10/71 and 3 1/7. This solution is still used today. He got this conclusion by circumscribing and inscribing a circle with 96 sides of regular polygons. However, two essential relations between the perimeters and areas of these inscribed and circumscribed regular polygons are required for the proof.

On the Sphere and Cylinder
Among many other geometrical discoveries, Archimedes confirmed that the volume of a sphere is two-thirds that of a circumscribed cylinder in Volume I of his work, On the Sphere and Cylinder.

Spirals
In The Spiral Archimedes squared the circle using the spiral. He also determined the area of one revolution (0<θ<2π ) of r = aθ

The area enclosed by the spiral arc of one revolution is ⅓ of the area of the circle with center at the origin and of radius at the end of the spiral arc.

FIBONACCI (1170 – 1240) 

Fibonacci also known as Leonardo Pisano Fibonacci, Leonardo of Pisa, and Leonardo Pisano Bigollo was born in what is modern day Pisa, Italy and iInterestingly enough, he also died there. (1170-1250) Fibonacci was an Italian mathematician and was known as the most ‘talented Western mathematician of the Middle Ages’.

Fibonacci spent most of his life in Pisa, where he studied mathematics. He wrote several books, which at the time, taught people the early basics of arithmetic. One of his many findings is explored in his book “Liber Abaci,” which became what is now universally known as the Fibonacci Sequence.

Fibonacci’s mathematical contributions are introducing the decimal number system into European roman numerals, the decimal positional system, algorithm and his most famous work:  

The Fibonacci Sequence

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, … 

This string of numbers is known as the Fibonacci sequence. The rule for generating new numbers in the sequence is simply that each following term is found by adding the two preceding terms together, so 1+1=2, 1+2=3, 2+3=5, etc.

The Fibonacci sequence is the oldest known recursive sequence. As previously stated, the sequence of each successive term can only be found by performing operations on the previous term. A closer look at the numbers that make up the Fibonacci sequence reveals a variety of captivating and intriguing patterns of mathematical features in nature. Fibonacci numbers typically arise in plant growth but can be found in numerous aspects of the environment:

All images are in the public domain.

LAGRANGE (1736 – 1813) 

Joseph-Louis Lagrange was born in Turin, Italy on January 25, 1736.  He died at age 77 in Paris, France on April 10, 1813. He became a respected Algebraist and Number Theorist.

Lagrange began working on a solution to numerous isoperimetric problems that were being discussed among the best European mathematicians at the time. He was 19 years old.

The Euler–Lagrange equations for Extrema of Functionals were derived by Lagrange, who was one of the founders of the Calculus of Variations. He further modified the concept to account for various limitations, resulting in the Lagrange multiplier method. This is a concept heavily encompassed in college level calculus III:

Lagrange was elected to the Berlin Academy of Mathematics in 1759 and began his career as a teacher there. He chose his brightest students to form a research society, which eventually became the Turin Academy of Sciences. This is one of Joseph Lagrange’s most significant accomplishments.

CONNECTING

Before the renaissance mathematics received little attention and progressed at a gradual pace. Religion and the afterlife were given increased attention and questioning scientific evidence was strongly discouraged and frowned upon.

During Renaissance mathematics and science began to progress and grow in the workings of isolated European mathematicians and scholars. The expanding population of humanist ideas led Europeans intellectuals to build off of and share the knowledge the scholars had developed. Mathematics was later implemented in the Scientific Method, thus amplifying the value of mathematics. Mathematics was in abundance, considering the numerous discoveries made.

Now mathematics is used in everyday life, because it provides stability, order, and precision into our daily lives. Mathematics develops skills such as spatial, and critical thinking, as well as the power of reason and is used universally across the globe.

References

  • All images are in the public domain. 
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  4. “The Teaching of Mathematics in The Renaissance.” Welcome to the Turnbull Serve
  5. Rothstein, Dave. “How Do Astronomers Use Math in Their Jobs? 
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  8. “The Teaching of Mathematics in The Renaissance.” MacTutor History of Mathematics.  Accessed April 13, 2022
  9. “History of the Roman Abacus.” Roman Math. Web. 13 April 2022.
  10. “Interesting Math History – Origin of Roman Numerals.” Retrieved from: Interesting Math History – Origin of Roman Numerals. Web. 13 April 2022.
  11. “Roman Achievements.” Roman Achievements. Web. 13 April 2022.
  12. “Roman Empire Timeline.” Retrieved from:  Roman Empire Timeline. Web. 13 April 2022.
  13. “Roman Mathematics – The Story of Mathematics.” Roman Mathematics – The Story of Mathematics. Web. 13 April 2022
  14. “Rome Reborn: The Vatican Library & Renaissance CultureMathematics.” Mathematics. Web. 13 April 2022
  15. Puzio, Raymond, J. Pahikkala, and D. Allan Drummond. “Euler-Lagrange Differential Equation (elementary).” PlanetMath. 4 Apr. 2010. Web. 13 April 2022
  16. Seikali, Nahla. “Joseph-Louis Lagrange.” UC Berkeley Department of Mathematics. Web. 13 April 2022 .
  17. Tong, David. “The Lagrangian Formalism.” David Tong: Lectures on Classical Dynamics. University of Cambridge, June 2008. Web. 13 April 2022.
  18. Weisstein, Eric W. “Lagrange Points — from Eric Weisstein’s World of Physics.” ScienceWorld. Web. 13 April 2022. 

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