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Fermat's Library
A platform for illuminating academic papers. We publish an annotated paper every week. Our chrome extension for arXiv:
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Fermat's Library 23h
Here's a visual proof that (2a+1)²=8Tₐ+1, where Tₐ is a triangle number Tₐ = 1+2+...+a ⚫️🔴🔴🔴🔴⚫️⚫️⚫️⚫️ ⚫️⚫️🔴🔴🔴⚫️⚫️⚫️🔴 ⚫️⚫️⚫️🔴🔴⚫️⚫️🔴🔴 ⚫️⚫️⚫️⚫️🔴⚫️🔴🔴🔴 🔴🔴🔴🔴🔵🔴🔴🔴🔴 🔴🔴🔴⚫️🔴⚫️⚫️⚫️⚫️ 🔴🔴⚫️⚫️🔴🔴⚫️⚫️⚫️ 🔴⚫️⚫️⚫️🔴🔴🔴⚫️⚫️ ⚫️⚫️⚫️⚫️🔴🔴🔴🔴⚫️
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Fermat's Library Feb 1
The Global Seed Vault located in Svalbard, Norway is a storage facility that holds more than 980,000 samples of crops, from almost every country in the world. Its purpose is to safeguard the world’s unique crop genetic material. 2.5 billion seeds may be stored in the Vault.
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Fermat's Library Jan 31
The battery symbol was inspired by the looks of voltaic batteries from the early 19th century.
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Fermat's Library Jan 30
In the 18th century, it was fashionable for men of an intellectual bent to have their portraits painted while wearing banyans and turban-like caps. They believed "loose dresses contribute to the easy and vigorous exercise of the faculties of the mind". Here's Euler's portrait.
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Fermat's Library Jan 29
In 1823, Niels Hendrik Abel managed to prove that there is no algebraic formula to solve equations of degree 5
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Fermat's Library Jan 28
The distribution of women and men across academic disciplines seems to be affected by perceptions of intellectual brilliance. Today's paper presents 4 studies performed to assess the perception of brilliance by young children aged 5 to 7. Insightful 🧐:
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Fermat's Library Jan 27
A visual proof A square inscribed in a semicircle has 2/5 the area of a square inscribed in the circle of the same radius. 🧐
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Fermat's Library Jan 26
An integral for the Golden Ratio 𝜙
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Fermat's Library Jan 25
Here's the remarkable coincidence that allows us to see total solar eclipses: the diameter of the Moon is 400 times smaller than the diameter of the Sun, but it is also 400 times closer to us.
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Fermat's Library Jan 24
Richard Feynman found trigonometry notation to be ambiguous and confusing. "If I had sin f, it looked like s×i×n×f" So he decided to create his own notation. See below. 🧐 What do you think?
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Fermat's Library Jan 23
When John Bardeen won the 1956 Nobel Prize in Physics, the Swedish king criticized him for not bringing his kids to the ceremony. He promised he would bring them the next time he won - and in 1972, he did when he became the first person to win 2 prizes in the same field.
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Fermat's Library Jan 22
It took us 255 years to go from Galilean transformations for falling bodies to Lorentz transformations that are in accordance with Einstein's special relativity.
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Fermat's Library Jan 21
This week's paper is a viewpoint article titled “World Scientists' Warning of a Climate Emergency” by William J. Ripple and 11.258 Scientists Signatories. Here's the paper:
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Fermat's Library Jan 20
Fermat dies in 1665 - his last theorem is unsolved ↓ ⏳88 y ↓ Euler proves it for n=3 ↓ ⏳72 y ↓ Legendre & Dirichlet prove it for n=5 ↓ ⏳14 y ↓ Lamé proves it for n=7 ↓ ⏳69 y ↓ Wolfskehl offers prize for solution in the next 100 years ↓ ⏳86 y ↓ Wiles proves it 🎉
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Fermat's Library Jan 19
The Williams-Kilburn tube introduced in 1947 was the first entirely electronic memory used in early computers. It used a cathode tube to store bits as dots on the screen's surface. Each tube could store about 1024 bits of data.
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Fermat's Library Jan 18
377 years ago Pierre Hérigone wrote a six-volume algebra text almost entirely in symbols, in which he first proposed the use of ⊥ (perpendicular) and ∠ (angle).
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Fermat's Library Jan 17
Tree Mountain is an artificial mountain near Ylöjärvi in Finland. Over a period of 4 years 11,000 people planted 11,000 trees in a specifically designed mathematical pattern based on the golden section. The project was conceived by the artist Agnes Denes in 1984.
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Fermat's Library Jan 16
This is the largest known Fibonacci number that's also prime, which is 21925 digits long and was proved prime by Mathew Steine and Bouk de Water in 2015.
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Fermat's Library Jan 15
Gustav Dirichlet (1805–1859) was a prodigy who at the age of 20 proved that Fermat’s Last Theorem has no solution when n=5
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Fermat's Library Jan 14
"Truth... is much too complicated to allow for anything but approximations" - John von Neumann
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