African Americans In Mathematics: Benjamin Banneker

                 Benjamin Banneker (1731-1806) of Baltimore County, Maryland was born a free man, but with plenty of familiarity to the brutality of slavery that was present at the time. Benjamin’s father, Robert, was a freed slave, and his mother, Mary, had parents who were both freed slaves. Mary’s mother, Benjamin’s grandmother, taught Benjamin to read at a young age and even pushed for Benjamin to be enrolled in a Quaker school. Benjamin’s school career did not last long, but his curiosity about mathematics was carried with him his whole life, a curiosity that would cause a great flow of scientific accomplishments.

Benjamin Banneker

          When Benjamin entered his twenties his passion for the sciences (ranging from mechanical engineering to astronomy) was bubbling. At this time, he had built a full sized grandfather clock modeled after a pocket watch, and was studying the cycles of eclipses. Benjamin continued to use his mathematical mind to create great things until his 40’s; by then, he built irrigation systems for his family farm, grain mills, and began to research bees and locusts. In 1772, the Ellicotts moved to a farm very close to the Banneker’s. The Ellicotts were Quakers; a faith that held that all races were equal and should be treated as such, and quickly noticed the brilliance of Benjamin Banneker.

            The Banneker family loaned many books to Benjamin, and encouraged him to begin calculating the exact times of eclipses to take place in the future. They also exchanged scientific research on surveying and much more. In 1791, Major Andrew Ellicott was asked to survey the land of Western New York by then Secretary of State Thomas Jefferson. Andrew suggested Benjamin as a more capable candidate for the position, and so began Benjamin’s rich correspondence with Thomas Jefferson.

            Benjamin became fairly close to Thomas, and wrote frequently about national issues and personal happenings. Benjamin quietly suggested that Thomas should do what he could to promote racial equality from his position in government. Some of these letters, along with scientific research, plans for cities, and personal commentaries were published in Benjamin’s Almanacs. The series of six annual almanacs were printed in the consecutive years leading up to the end of his life, and was the pinnacle of his scientific career.

The cover of Benjamin's 1795 Almanac

           

Sources:

https://en.wikipedia.org/wiki/Benjamin_Banneker#Mythology_and_legacy

http://www.biography.com/people/benjamin-banneker-9198038#early-years

Images

http://johnhopebryant.com/2012/02/black-facts-in-history-benjamin-banneker.html

http://www.pbs.org/wgbh/aia/part2/2h68b.html

Everyday Math: Architecture

Throughout this series, we have discovered mathematics posing as a character on your favorite television show, hiding in your favorite pieces of art, and starring in your favorite big-screen productions. We have even uncovered math in the baseball diamond, at the casino table, and on the soccer pitch.. but we aren't done yet. This Everyday Math blog post goes even further to examine the mathematics behind the very building you are sitting in, and the people who designed it.

That's right– let's take a look at the math behind architecture!

According to the dictionary, architecture is the art or practice of designing or constructing buildings. While this is common knowledge, the close correlation between mathematics and architecture might go unrecognized. The connections between the two disciplines are almost innumerable, especially when you realize that both, in a way, are the study of patterns and systems. Throughout history, some of the greatest architectural feats have been based in the realm of mathematics. This post will further explore some of these buildings, as well as the connection between math and architecture.


The first instance in history that demonstrates a mathematical association to architecture involves, not surprisingly, Pythagoras. Known for being the mind behind the Pythagorean theorem, numbers held a special significance to the Greek mathematician. This significance was mainly geometrical, as Pythagoras spoke of square, oblong, and triangular numbers. He also placed an importance on the aesthetic qualities of numbers and proportions. After Pythagoras's death, his followers– the Pythagoreans– carried on his ideas and utilized them in 447 BC when rebuilding the Parthenon. The ratio 3 : 4 : 5 was used throughout the building of the Parthenon, and later was notated as one of the Pythagorean Triples. Further, the ratio between the height and width (4 : 9), is the same as the ratio between the width and length (4:9). This may not seem significant but Berger, a mathematician, examined that the ratio 4:9 is used in the creation of the columns, as well as the inner area of the temple. Many argue that this consistent ratio accounts for the aesthetic beauty of the temple.

Let's turn the history book ahead a few hundred years. Time– 27 BC. Place– Ancient Rome. In case you dosed off during a few months of History class, there are many consistencies between the societies of Ancient Greece and Ancient Rome. Like Ancient Greece, Rome focused on education, the arts, and beauty. This sets the stage for more architectural accomplishments, and with that more mathematical connections. In fact, in his series of books titled De Architectura, Virtruvius outlines the practical applications of mathematics that are necessary for building design.  The Classical age again mirrored the former great civilizations in Greece and Rome, creating buildings that relied again on the importance of proportions, ratios, and perspective. The Classical age brings us Brunellischi, Alberti, and Leonardo da Vinci– all fascinated with mathematics. 

London City Hall– Created by Foster + Partners
Note the helical staircase inside

After that nice history lesson, you may be wondering.. Why should I care? Throughout history, math was needed to properly structure buildings. As we mentioned, the two areas of study were completely intertwined. Today, technological advancements (like calculators!) help architects with some of the work load. However, in many architectural projects, these technological advancements are still set in place through mathematics. 

One of today's most famous architecture studio is Foster + Partners. The company is famous for constructing enormous structure that dwarf their surrounding buildings. With the added size, comes more of a need for math. The buildings need to be made secure, aesthetically pleasing, comply with building regulations, and maximize a budget. A series of equations and programs help to ensure all of these categories are fulfilled. The Special Modeling Group's (SMG) was created to maximize the efforts of architects. SMG's often build larger shapes from smaller shapes. Makes sense, right? In order to do this, they create equations for various sections of a building. Examples of this are pictured below. 

Has this post convinced you of the connections between mathematics and architecture? 

In case it hasn't, here are some testimonials from architects further explaining their personal opinions.

(Testimonials gathered from http://www.lifeofanarchitect.com/architecture-and-math/)  



Jes Stafford
"Architects should be math ninjas. The aspiring architect should rush headlong into math as if charging into a field of battle. Math is an education in problem solving and of knowing what is asked. There are few stronger parallels to all the the variables in the Builder-Architect-Client dynamic. All math puns intended."

Andrew Hankins
"Math is important to my daily tasks as an Architect. It mostly involves simple calculations, but for me, it is necessary to be able to do them quickly in my head.  And they are mostly simple equations, but it definitely helps if you can do them in your head and on the fly."

Evan Troxel
"That said, it is better if you are decent at math. Here are some examples people usually don’t think of as math, but are things architects use all the time: We are constantly adding and subtracting measurements, thicknesses, volumes and areas. We are responsible for budgets. We work with spreadsheets that tally sizes of spaces and everything has to all add up. We do TONS of geometry, and we love it. Geometry is math, right? Yes it is. Drawing + Math = Awesome. That’s one reason we’re architects and not artists."


Sources: http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Architecture.html
https://plus.maths.org/content/perfect-buildings-maths-modern-architecture
http://www.lifeofanarchitect.com/architecture-and-math/

Martin Luther King Day

Martin Luther King Day

      In honor of Dr. King’s work towards African American equality, here is some information about Elbert Frank Cox, the first African American to receive a Ph. D in mathematics.

http://www.aaregistry.org/

      Elbert Cox was born in Evansville, Indiana in 1895. His father had spent time at Indiana University completing graduate work, and Cox soon followed in his father’s footsteps attending Indiana University for his undergraduate degree. Despite his achievement in the field of math, Cox was subject to unfair treatment due to his race. His college transcript was imprinted with the word “colored” and in 1921 he was denied admission to Cornell due to a recommendation letter describing concerns about his race. However, after receiving the Erastus Brooks Fellowship in 1922, he enrolled in Cornell University. In 1925, he became the first African American to receive a Ph. D in mathematics and was recognized on a national and international level. Cox passed away in 1969, after a 40-year career of teaching and inspiring other young mathematicians. Elbert Cox is honored annually at the National Association of Mathematicians meeting through the Cox-Talbot Address.

     

Stay tuned to our social media pages for more in depth information about African American mathematicians as we celebrate the upcoming African American history month in February!

References: www.math/buffalo.edu

Thanksgiving: Facts and Figures

With Thanksgiving approaching this week, we wanted to take a look at a few numerical facts and figures about the holiday. Keep reading for a text version of all the content in the image, plus more!

Throwback Fact: Thales of Miletus

Thales of Miletus was an ancient Greek mathematician, scientist, and philosopher who predated most well known Greek thinkers. Though his contributions and discoveries in physical sciences and philosophy were noteworthy, this is the Center of Math, and thus we are going to focus on his contributions to mathematics for this week's Throwback Fact.  So, keep reading to learn more!

Thales
Source: Wikipedia

Throwback Fact: The SAT

This Saturday marks the first SAT exam of the year, so to celebrate, the Center of Math is going to talk about the history of the SAT for this week's Throwback Fact. Keep reading to learn more about the SAT!

Throwback Fact: The ACT

With the first ACT exam quickly approaching--this Saturday, in fact!--the Center of Math wanted to talk about the history of the ACT and how it has evolved over the years. Although the ACT has not been around as long as the SAT, it has become just as popular and is now accepted by all universities and colleges in the US.

Throwback Fact: The Equals Symbol

For this week Throwback Fact we decided to investigate the origins of the equals symbol. You may be surprised, the equals symbols hasn't been around for as long as you may think.

Where did the equals symbol come from?

Throwback Fact: Mancala

An example of a modern Mancala board from Europe
Source: https://en.wikipedia.org/wiki/File:Bao_europe.jpg

        Many historians believe that Mancala is the oldest board game in existence. Since Mancala is one of our favorite games in the office we decided that for the throwback fact of the week we would take a look at Mancala.

        Mancala is a/the term used to describe a collection of similar games, of which there are over 800 around the world. Some of the variations include Bao, which is played across the east coast of Africa, Oware, which is played in the Caribbean, and Kalah, which is the modern game played in the US and Europe, which we call Mancala. It is unclear exactly where Mancala originated but many historians believe it was in Africa where players used to carve holes in the ground and use pebbles to play.

Bao players in Zanzibar 
Source: https://en.wikipedia.org/wiki/File:Bao_players_in_stone_town_zanzibar.jpg

        There are many different theories as to what the original purpose of the game was for ancient people. One theory is that it was a record keeping system used to manage debit and credits, which were represented by the two sides of the board. Another theory is that Mancala was a ritual at funerals, weddings and other ceremonies. It could also have just originated as a game, which is its main use now.

        Whatever the origins of Mancala one thing is for sure, ancient people needed to count to play, just like we do now. Mancala is a great game for teaching kids how to count and work on strategic thinking skills as they age. 

Tell us, what are some of your favorite board games?

Source: 1, 2, 3

Throwback Fact: Ada Lovelace and the Analytical Engine

Portrait of Ada Lovelace
image: commons.wikimedia.org

Ada Lovelace was born in London, England in 1815 to a poet father and math-loving mother. After her father left the family when she was just four, Ada’s mother raised her on a strict regiment of science, logic, and mathematics. Due to this she developed an early love for machines and technology, a passion that would lead her down a path of scientific discovery. 

Relationship with Charles Babbage:

In 1833, at around seventeen, Lovelace was introduced to Charles Babbage, a mathematician and inventor who was famous for his work with calculating machines. Babbage became a mentor to Lovelace who was captivated by his innovative work. Soon, Babbage would ask Lovelace to work with him on his newest invention called the Analytical Engine, which was meant to perform mathematical calculations just like a computer.

Lovelace’s Work:

Babbage asked Lovelace to translate an article on the analytical machine written by Italian engineer Luigi Federico Menabrea. While translating the text from French to English, she also added her own thoughts and ideas on the machine. She theorized that the machine could repeat a series of instruction, a process known as “looping” that is still used today by computer programmers. She also created codes so that the device could handle numbers, letters, and symbols. Due to these findings and theories, Lovelace is often considered the first computer programmer. 

Lovelace’s Legacy:

Ada Lovelace envisioned a world where machines would be an integral part of human imagination. At the time, these ideas where dismissed by the scientific community because they were too difficult to comprehend. Just like many other visionaries of her era, only time and knowledge could lead to the acceptance of her work. In the 1970’s, engineers at the United States Department of Defense, inspired by her work on the calculation of Bernoulli numbers, named a computer programing language Ada in her honor. Today, Lovelace also serves as an inspiration to many women in the STEM fields, who see her as a visionary who lived before her time. They celebrate Ada Lovelace Day on the second Tuesday of October in her honor. 

Sources: 1, 2

Counting Systems: Maya

The great pyramid at the Mayan city Chichen Itza
(it was featured in one of our favorite blog posts)

The Region: The Mayan civilization can be split up into several distinct periods: the preclassic, classic, and postclassic. During the final period, explorers from Western Europe made their first contact with the Mayan people (around 1500 CE). 

Over the 3500 years that the Mayan culture was prominent, the lands under their control remained expanded and shrank several times. They were limited to the Yucatan Penninsula (present day, a part of Mexico) but had strong ties to the Olmec and Toltec cities in surrounding Mesoamerican lands.

The Numerals: In many ways, the Mayan numeral system is more intuitive than our own. They used a Base-20, or vigesimal, system.

Counting Systems: Ancient China

Shards of the Shang Oracle Bones

In the 1890s, an archaeological dig in the Henan province of China unearthed a treasure trove. A set of bones carved with ancient text were dug up where the capital of the Shang Dynasty (1600 - 1046 BCE) was located. The oldest inscriptions that are recognized as Chinese were carved in about 1200 BCE on these ancient "Oracle Bones."

The Region: Chinese history is vast. There have been groups living in China for thousands of years, and we've discovered written records about the established dynasties on the Eastern side of the country dating as far back as 1200 BCE. The cultural center of China was naturally isolated, with mountains on the west and water to the east. This allowed Chinese numerals and mathematics to develop naturally, without much influence by other number systems, for centuries.