Today I saw this problem on Medium:
Compute the limit
Followed by “Pause the article and attempt a solution now.” (Don’t cheat and look ahead)
So I did. I do not really like factorials, so I immediately thought of Stirling’s approximation:
ln n! ≃ n ln n – n as n → ∞
and all of the n‘s cancelled, leaving the result 1/e. I then looked at the author’s solution. My answer was correct,
but he used a completely different approach, as you can see. I posted my solution, and got a nice complement from him.
This is Thanksgiving day in the USA. I am thankful that my calculus skills are still pretty good decades after my last formal course in that or any related field .
Inventing the Flat Earth: Columbus and Modern Historians, by Jeffrey Burton Russell, is the book for the day. Columbus did not show the world that the Earth was round. No educated European in 1492 believed that the Earth was flat. They all knew it was round. As all math geeks know, Eratosthenes of Cyrene had made a good calculation of the circumference of the Earth about 200 BCE.
Catholic church authorities did not say that the plan of Columbus to reach the orient by sailing westward was impossible because the Earth was flat. Their scholastic theology was based on the philosophy of Aristotle, who understood perfectly well that the Earth was round.
There are passages in the Bible that suggest a flat Earth, but almost all theologians of ancient and medieval times knew the evidence for a round Earth was overwhelming, and understood the Bible was not to be taken literally in this and similar cases.
The objection to the plans of Columbus was that, thanks to Eratosthenes, people had a good idea of the distance from the west coast of Europe to the east coast of China, and could easily calculate that no ship of the day could possibly carry enough supplies for the voyage.
Columbus, acting like a 21st century Republican, rejected the best science of the day and chose a smaller alternative value for the circumference that suited his purposes. He was just lucky that the Americas happened to be there. As a result their inhabitants were then horribly unlucky.
The story about Columbus and the flat Earth is a 19th century invention, not history.
Also posted on Facebook.
Irish Class, February 22, 2016
Rang Gaeilge, 22ú lá mí Feabhra 2016
‘The Interview’ Brings In $15 Million on Web
LOS ANGELES — “The Interview” generated roughly $15 million in online sales and rentals during its first four days of availability, Sony Pictures said on Sunday.
Sony did not say how much of that total represented $6 digital rentals versus $15 sales. The studio said there were about two million transactions over all.
So the answer to the 2012 opinion piece
Is Algebra Necessary? is YES!
From Dan Meyer,