Do you believe the Earth is round? How do you know? Have you seen pictures from outer space? Read mathematical proofs? Or you just never questioned your beliefs before? It’s hard to think of another fundamental scientific truth like the round Earth model so many people accept.

It shouldn’t come as a surprise that the ancient Greeks first proposed that the Earth was round. Renowned philosopher Pythagoras conjectured the spherical model around 500 B.C., though purely based on non-empirical or “because-I-said-so” reasoning. Most other Greeks accepted his conjecture but struggled to put empirical evidence or numbers to their intuitions. Aristotle noticed practical consequences of the round model a century and a half later such as ships disappearing hull first beneath the horizon, the periodic rotations of the constellations, or the Earth’s round shadow projected on the moon in a lunar eclipse. The first concrete, numerical evidence did not come until around 240 B.C. when Eratosthenes first proposed a value for the Earth’s circumference [1]. His circumference value only deviates 0.5 to 17 percent from modern measurements and is thus considered legitimate [2]. As with some ancient relics, no primary account of Eratosthenes method exists. His methods survive through Cleomedes’s On the Circular Motions of the Celestial Bodies, a work historians deem potentially biased on mathematical, historical, and linguistic accounts [3]. However, Cleomedes’s text remains valuable to historians and scientists alike for preserving one of the most concrete, paramount experiments in science.

Eratosthenes’s method used a few geometrical proofs and a short experiment dependent on one natural phenomenon: the sun shining directly down an Egyptian well in Syene, now Aswan [1]. Because he could not see a shadow at the bottom of the well, he knew the sun’s rays traveled directly down the well. Eratosthenes travelled to this well during the summer solstice, when the sun shines the longest due to the Earth reaching its maximum tilt towards the sun. Just by using his geometric knowledge and a short experiment in Alexandria, he arrived at a fairly accurate circumference measurement.

Of course, Eratosthenes made a few assumptions along the way. First, the distance between Alexandria and Syene was 5,000 stadia or 568 miles apart (Figure 1a). Instead of Google Earth, Eratosthenes employed professional walkers of the time to measure this distance. Second, Syene and Alexandria were located on the same meridian, or longitudinal line connecting the Earth’s north and south poles [3] (Figure 1b). Third, the sun’s rays struck the Earth parallel to each other due to the sheer distance between the Earth and sun. He used these three assumptions to create an elegantly simple natural system and means of calculating circumference from it (Figure 1c).

Eratosthenes’s calculated red angle 𝜃 theta in his Alexandrian experiment. He applied the simple trigonometric formula tangent to find 𝜃 knowing the statue’s height and by measuring its shadow (Figure 2).

Eratosthenes then applied the alternate interior angle theorem, which states that alternating, interior angles formed by two parallel lines crossed by a third, straight line will be identical.

In short, this theorem justified that his measured 𝜃 was indeed the same angle between Syene and Alexandria relative to the center of the Earth (Figure 3).

Now, Eratosthenes used the formula for arc length as:

𝑎𝑟𝑐 𝑙𝑒𝑛𝑔𝑡ℎ=𝑟𝑎𝑑𝑖𝑢𝑠 × 𝜃,

where arc length represented the 5,000 stadia distance between the two cities to find radius 𝑟. Multiplying the radius by 2π yielded the Earth’s circumference. So, although Eratosthenes’s value might not look as simple and elegant as a NASA image, it was monumental in that he proposed the first numerical justification of Pythagoras’ model.

Today, it’s hard not to accept the round Earth model. NASA images from outer space physically show the Earth’s spherical shape. Modern technology like the internet and airplanes rely upon the round Earth model due to the communication of satellites orbiting the Earth at various positions and times. Even though this substantial amount of proof is enough for many to accept a round earth, some minds need further persuasion. Let’s take a closer look into the perspectives of those who disagree with this spherical model.

A study on the flat Earth trend in social media traces the history of the flat-Earth movement and investigates the support and propagation of its ideology [4]. From a scientific perspective, many flat-Earthers uphold the discredited work of Victorian English scientist Samuel Birley Rowbotham. In his Bedford Level experiment, Rowbotham appeared to observe a flat curvature of the Earth by measuring the change in height of a stationary ship mast as he sailed down a river. His peer physicist Alfred Russel Wallace repeated the experiment and subsequently disproved Rowbotham’s experiment. Rowbotham’s error ultimately stemmed from atmospheric refraction, changes in air density bending light near the surface of the earth. Perhaps Rowbotham observed a flat earth due to atmospheric refraction and the Earth’s curvature bending light in equal but opposite directions. Although changes in air density caused atmospheric refraction in Rowbotham’s experiment, light bends under other circumstances in everyday life. Try putting half of your hand in some water. Look down at your hand. It looks bent, right? Like water, air is a fluid and can distort an object’s true position. Considering this vital factor, Wallace arrived at the accepted curvature [5].

Yet, just as Wallace disproved Rowbotham, some modern flat-Earthers discredit Wallace. The movement uses the Bedford Level experiment among other methods as scientific justification for their beliefs. And naturally, many flat-Earthers remain plain skeptical of mainstream beliefs. Often, the movement selects key authorities like engineers, government officials, or pilots to back their claims. Others hesitate to trust large, government establishments or celebrity figures.

Although flat-earthers draw upon flawed scientific experiments, skepticism, or other means of unconventional proof in order to maintain their beliefs, those who accept the round earth let the millennia of scientific proof determine their beliefs instead. The ancient work of Pythagoras, Aristotle, and Eratosthenes weaves a rich tapestry of human achievement which laid the foundation for physical high-resolution images of the Earth itself. The trust of this model is not rooted in blind belief but instead is ingrained in empirical evidence that holistically encompasses tangible factors all around us. Granted, most people do not think twice about natural phenomena like a round Earth or atmospheric refraction. Yet such factors represent the intricate inner workings of the natural world and demonstrate the impact all phenomena have on our everyday perceptions.

As scientists continue to discover more exciting, novel knowledge, it is easy to forget what our predecessors discovered and learned in the past, especially when the information was not well-documented through generations. Just like the Earth, what comes around, goes around. Future generations will move forward with our work through the methods of logic, experimentation, and evolution we leave behind. Each celestial rotation renews the promise of discovery but also reaffirms humanity’s legacy of scientific excellence anchored by our Greek ancestors.

References

[1]: Tretkoff, Ernie. “This Month in Physics History.” Edited by Alan Chodos and Jennifer Ouellette, American Physical Society, June 2006, www.aps.org/publications/apsnews/200606/history.cfm#:~:text=240%20B.C.%20Eratosthenes%20Measures%20the%20Earth&text=By%20around%20500%20B.C.%2C%20most,method%20of%20estimating%20its%20circumference.

[2]: Britannica, The Editors of Encyclopaedia. “Eratosthenes”. Encyclopedia Britannica, 22 Jan. 2021, https://www.britannica.com/biography/Eratosthenes. Accessed 21 April 2021.

[3]: Sidoli, Nathan, and Christian Carman. “Mathematical Discourse in Philosophical Authors: Examples from Theon of Smyrna and Cleomedes on Mathematical Astronomy.” Instruments, Observations, Theories Studies in the History of Astronomy in Honor of James Evans, edited by Alexander Jones, 2020, pp. 213–229.

[4]: Paolillo, John C. “The Flat Earth Phenomenon on YouTube.” First Monday, vol. 23, no. 12, 27 Nov. 2018, doi: http://dx.doi.org/10.5210/fm.v23i12.8251.

[5]: “Bedford Level Experiment.” Wikipedia, Wikimedia Foundation, 8 Apr. 2021, en.wikipedia.org/wiki/Bedford_Level_experiment.