Johann Elert Bode

Bode's interest in astronomy, mathematics and geography started in 1765 when his father's personal physician Heinrich Reimarus introduced him to Johann Busch, a professor of mathematics from Hamburg. With the help of Busch, Bode wrote and published a book entitled “Bode 1766”. Bode started conducting formal studies in astronomy and mathematics at an early age of 19. Among his early notable observations includes the “Venus Transit” in June 1769 and “1770 Comet”. In 1768, Bode published his second book entitled “Instruction for The Knowledge of the Starry Heavens”. The book was released in multiple editions. The second edition of the book contained thorough observations on the “Empirical Law of Planetary Distance” which was initially revealed by J.D Titus. Bode applied some of Titus' conclusions and finally named it as the Titus-Bode Law during the late 17th century.

Bode went to Berlin in 1772 after accepting the job of teaching math and astronomy at the Berlin Academy of Sciences. The academy's astronomy head and Berlin Observatory Chief Director Johann Bernoulli became impressed with his interpretation on the calculations of the “Schlesien Calendar” by Christine Kirch. He worked with Christine's great grandfather Gottfried Kirch and Lambert for the foundation of the “German Astronomical Yearbook and Ephemeris” in 1774.

In July 1774, Bode married Johanna Lange, a close relative of the Kirch family. Lange died after giving birth to their fourth child. In 1783, Bode married Sophia Dorothea, Lange's oldest sister. Bode married Charlotte Lehmann after Dorothea's early death. He retired from the Berlin Observatory in 1825 after four decades of serving under the directorial position. A year after his retirement, Bode died in Berlin at the age of 79.

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Ptolemy

Ptolemy wrote down his work in a long, thirteen-book treatise called the Almagest. This compilation was considered very important and influential to other mathematicians and scientists in those early times. It was translated into Arabic and then Latin, and made accessible to many people. For present-day students, it presented an exact account of Ptolemy's discoveries and contributions to science.

In the Almagest, Ptolemy wrote of his mathematical studies regarding the motions of the planets, the sun and the moon. He presented the so-called geocentric theory, which stated that the earth was the center of the solar system, and that the other planets and the sun revolved around it. This has now been proven to be untrue, of course, but Ptolemy, based on that earth-centered theory, managed to come up with a sophisticated mathematical model that predicted with surprising accuracy the motions and positions of the planets. Because it made sense, as Ptolemy had demonstrated, the earth-centered model of the solar system prevailed for about fourteen centuries.

In his calculations, Ptolemy came up with the value of pi = 3.14166, using trigonometric methods. He also introduced many geometrical theorems and proofs.

Aside from the Almagest, Ptolemy authored other writings, including the eight-book Geography and a work on Optics. He tried to map the known world, using latitudes and longitudes, but there were many inaccuracies in his work. The scarcity of reliable empirical data in those times helped to justify the errors, but doubt had begun to be cast on Ptolemy's works.

Later, many scientists hurled accusations against Ptolemy's methods and writings. There were accusations of fraud, that Ptolemy doctored some of the empirical data and observations he used to make them fit his mathematical models. There were also accusations of plagiarism, that Ptolemy copied earlier works by Hipparchus and other mathematicians. Tycho Brahe, Laplace, Lalande, Delambre, and Isaac Newton were some of the prominent scientists who criticized Ptolemy's work.

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Photo by: Creative Commons

Hipparchus, a famous Greek mathematician and astronomer, was born in 190 BC in what is now Turkey. He may not be as famous today as Euclid, Pythagoras and other Greek luminaries, but during his time, he was greatly renowned. His mathematical achievements were considered exceptional by his contemporaries and many future generations. Simply put, he was a legend, and his face adorned coins that were in circulation for many decades in that period.

Hipparchus holds the distinction of developing trigonometry. He made what is arguably the earliest trigonometric table. This table provided an effective method to solve trigonometric problems. Hipparchus was also the first person to bring to Greece the idea of dividing a circle into 360 degrees.

In addition to trigonometry, Hipparchus also excelled in calendrical and astronomical studies. He made a star catalogue that continued to be used for a long time by future astronomers. It consisted of no less than 850 stars, with all their positions and movements accounted for. Hipparchus also made very accurate calculations of the solar year and the equinoxes. They were so accurate that the difference between his calculated year length and its present-day equivalent is less than 6.5 minutes.

Another valuable contribution of Hipparchus was his discovery of precession, which has to do with the axis of earth's rotation. Hipparchus was able to prove that the direction of this rotation changed slowly in time. This was significant in astronomical studies. It gave rise to two different kinds of year: the sidereal and the tropical.

Hipparchus also studied the moon and its motions. He was able to calculate with great accuracy the distance of the moon from the earth. He made use of empirical data and shrewd mathematical calculations to come up with his measurements.

Overall, Hipparchus managed to transform astronomy from being a largely theoretical study into a practical and predictive science. He demonstrated that careful observation and mathematical calculations, when combined, could predict the movements and positions of stars, the earth and the moon.

Clearly, Hipparchus was a mathematical and scientific genius. In his honor, a lunar crater has been named after him, the Crater Hipparchus. Another crater on the planet Mars also bears his name.

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Eratosthenes

Eratosthenes is famous for many things, including a mapping method that used latitudes and longitudes, and his accurate computation of the circumference of earth. To compute for the circumference of the earth, Eratosthenes used the principles of trigonometry and available data on the altitude of the sun in two specific locations at noontime. He worked on the assumption that because the sun was very far from earth, its rays could be considered parallel.

He then used the sun's positions from two known, different locations to come up with 252,000 stadia as the size of earth. Roughly, this translates to about 40,000 to 46,000 km; the actual earth circumference is about 40,000 km.

Erathosthenes also introduced a method of finding prime numbers, which to this day bears his name (the “Sieve of Eratosthenes“). He further gave accurate measurements of the distances of the earth from the sun and from the moon. He compiled a star catalog that consisted of 675 stars. He made maps of Egypt and other important centers of civilization. He too was the first to coin the word “geography.” And he invented a device called the armillary sphere. As can be seen, he excelled in many branches of learning, especially in astronomy, arithmetic, geography and even music.

Despite his many achievements, Erathosthenes acquired the rather insulting nickname “Beta.” He was also called “Pentathlos”, which meant a well-rounded and accomplished athlete, but one who never got first place. Erathosthenes did make many important discoveries and contributions to science, but he always came up second to someone else. He never became the foremost authority on any discipline, but always the second, the runner-up, or the beta. It didn't help that Erathosthenes had a rather eccentric and haughty character, which probably turned off some people.

Eratosthenes became blind in the latter part of his life. This must have proven to be a serious impediment to his scholarly work, discouraging him greatly. A year later, he committed suicide by starving himself to death.

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