How Eratosthenes measured the earth: part 4 of 4.

The angle of the sun is the last hurdle Eratosthenes had to overcome with his data collection methods.

Here we review the popularly believed story -- measuring shadows of sticks -- before looking at a more likely and methodologically simpler alternative.

Concludes with a bibliography.

(Reading time: 15 minutes)
#ancientscience #eratosthenes #geography #ancientgreece
https://kiwihellenist.blogspot.com/2023/07/eratosthenes-4.html

How Eratosthenes measured the earth, part 3 of 4: distance.

How did Eratosthenes find out the distance from Syene to Meroë? What units did he use, and what do they mean in modern units?

(Reading time: 18 minutes)
#ancientscience #eratosthenes #geography #ancientgreece
http://kiwihellenist.blogspot.com/2023/06/eratosthenes-2b.html

The ongoing story of how Eratosthenes measured the earth, based on ancient evidence. Part 2b: distance.

How did Eratosthenes find out the distance from Syene to Meroë? What units did he use, and what do they mean in modern units? What's the difference between the 'metrological stadion' and the 'itinerary stadion'? (And how do they compare to the kilometre and the 'itinerary kilometre'?)

(Reading time: 18 minutes)
#ancientscience #eratosthenes #geography #ancientgreece
https://kiwihellenist.blogspot.com/2023/06/eratosthenes-2b.html

Despite limited technology and resources, ancient scientists used empirical data learn about the world and come up with accurate hypotheses.

Spices were highly valued by early foodies.

Transparent communication, aligning incentives, and reconciling data with lived experience is crucial for success.

https://paninid.substack.com/p/cristoffa-corombo-was-bad-person

#STEM #scientificmethod #Eratosthenes #Ptolemy #LibraryofAlexandria #discovery #communication #transparency #datainformed #productmanagement #foodies #spices

How Eratosthenes measured the earth: an account grounded in ancient evidence.

Part 2a explains the basic idea underlying the measurement, and begins to look at the hurdles involved in obtaining observational data.

Parts 2b and 2c will look at what we know about measuring overland distances, and 2nd century BCE instrumentation for observing the angle of the sun.

(Reading time: 16 minutes)
http://kiwihellenist.blogspot.com/2023/06/eratosthenes-2a.html
#ancientscience #eratosthenes #geography #astronomy #egypt #ancientgreece

🪷 #Eratosthenes says on 11 June 1184 BC Greeks sacked Troy by sneaking through the gates inside the Trojan Horse. Other sources say it was 24 April 1184 BC. #TrojanHorse art by #AngusMcBride. 🪷

How Eratosthenes measured the earth. Part 2a.

The ongoing story of Eratosthenes' measurement, grounded in ancient evidence.

Part 2a: the basic principle of the measurement; an introduction to the technological hurdles; and the problem of simultaneous measurements.

(This was _not_ a problem to be solved by two sticks!)

(Reading time: 16 minutes)
#ancientscience #eratosthenes #geography #ancientgreece
https://kiwihellenist.blogspot.com/2023/06/eratosthenes-2a.html

The length of the stadion, the ancient Greek distance unit, has had a lot of ink spilled over it.

Most of the confusion relates to conversion with Egyptian units, and selective citation. The schoinos was wilidly inconsistent. Eratosthenes' stadion works out to anywhere from 157.5 m to 262.5 m depending on how you calculate it.

When Pliny expresses Eratosthenes' stadia in terms of Roman miles, suddenly they're much more consistent with other reports.

#geography #classics #eratosthenes

Eratosthenes' wobbly Alexandria meridian.

In the mid-200s BCE Eratosthenes invented the device of lines of longitude and latitude. The Alexandria meridian held a central place in his account of the geography of the known world.

Key locations on the meridian: Olbia (Ukraine), Lysimacheia (Türkiye), Rhodes (Greece), Alexandria (Egypt), Syene (Egypt), Meroë (Sudan).

#geography #eratosthenes #ancientegypt #ancientgreece #classics

🪷 #Eratosthenes says on 11 June 1184 BC Greeks sacked #Troy by sneaking through the gates inside the #TrojanHorse. Other sources say 24 April. Centuries later #French #historical #comicbooks heroes #Alix & #Enak find it along with a #Trojan plot for revenge! #comics #comicbookart. 🪷

How Eratosthenes measured the earth. Part 1: the discovery of the earth's shape.

Before 400 BCE, everyone was a flat-earther. Afterwards, it gets hard to find people who weren't aware that the earth is round.

A look at early Greek thought on the shape of the cosmos, the earth's location, and the angle of the ecliptic, leading up to the first estimate of the earth's size in Aristotle.

(Reading time: 18 minutes)
https://kiwihellenist.blogspot.com/2023/04/eratosthenes-1.html
#ancientscience #eratosthenes #geography #ancientgreece

☀️📐 https://thekidshouldseethis.com/post/eratosthenes-earth-circumference-carl-sagan-video

"#Eratosthenes’ only tools were sticks, eyes, feet, and brains,
plus a taste for experiment. With them he deduced the circumference of the #Earth with an error of only a few percent, a remarkable achievement for 2,200 years ago." ✨🌍✨

#CarlSagan #video #math #science #geometry #history #storytelling #cosmos #sun #shadows

One day, one decomposition
A003309: Ludic numbers: apply the same sieve as Eratosthenes, but cross off every k-th /remaining/ number

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/Ludic_numbers.html
2D #graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/Ludic_numbers.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #ludic #numbers #sieve #Eratosthenes #remaining

Playing more with #ChatGPT... I asked it to write a Sieve of #Eratosthenes in #R. I was initially impressed... then, not so much.

https://slinberg.net/posts/2022-12-06-chatgpt-sieve/

a rough diagram showing how #Eratosthenes was able to 1) discover the earth was round and 2) calculate its radius... 2000+ years ago

#archimedes #plato #eratosthenes #copernicus