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628 AD after the aforementioned battle the Persians are forced to a peace treaty concluding a war that lasted for more than two decades. There won't be another war; soon both empires will have to face the danger of annihilation from Islam.

Interesting... I am studying Persian History right now, and trying to learn Farsi... which leads me to:
629... in my Farsi textbook, the page that deals with pesky transitive verbs.

630 the lowest hexagonal number that is the sum of 6 consecutive primes

also a popular time set on alarm clocks

TheFlyingBoat wrote: ↑

Tue Jan 19, 2021 1:44 am

90kicvesb wrote: ↑

Mon Jan 18, 2021 10:15 pm

Contrary to what one might think at first glance, X^4 + 1 does indeed have a polynomial factorization with real coefficients.

626 = (25 + sqrt(2)*5 + 1) * (25 - sqrt(2)*5 + 1)

I will note that no one disagrees or thought that x^4+1 can be factorized over R. It's factorization over R is relatively straightforward:

(x^2-sqrt(2)*x+1)(x^2+sqrt(2)*x+1).

When people say that x^4+1 is irreducible they meant that there is no reduction over Q, the field of rational number, of which root 2 is not one. x^4+1 has no real roots nor is it reducible in Q.

627 featured the famous battle of Nineveh in which the Byzantines cross the Great Zab to defeat the Sassanid Empire.

Amusingly x^4 + 1 is reducible in every completion of Q except Q_2

dargorygel wrote: ↑

Tue Jan 19, 2021 2:54 pm

Interesting... I am studying Persian History right now, and trying to learn Farsi... which leads me to:
629... in my Farsi textbook, the page that deals with pesky transitive verbs.

Any particular reason to learn Farsi?

631 is the number we have reached, we should have been at 705!

631 the second lowest centred triangular prime number that is also a centred hexagonal number. The lowest is of course 19.

632 AD

The year of death of the prophet Muhammad, his daughter Fatimah and son Ibrahim

633 Squadron

Novel by Frederick Smith subsequently made into a film with a popular soundtrack composed by Ron Goodwin

Soundtracks are my preferred kind of music. I will check it out.

634 King Cadwallon of Gwynedd assassinates Eanfrith of Bernicia and his bodyguard while attempting to negotiate peace (this is a man to trust!).

635f... John Deere's 35 ft cutting platform, for harvesting and such. I dream...

(@Prince William)... learning Farsi because it is there to learn!

(but there are hundreds of languages, why Farsi?)

636 AD On April 4 dies Saint Isidore bishop and patron saint of Seville.

637 ad... The siege of Jerusalem, part of the war between the Byzantine Empire and the Rashidun Caliphate.

(I try to loosely learn a language every year or so. I have a Persian (Iranian) friend who has been pushing Farsi for years.)

638 AD Jerusalem is captured by Arabian Empire. It must be one of the cities that changed it's ruler so many times.

(Farsi is a good language to learn because it is very close to other languages of the region. From internet: Persian is one of the most important members of the Indo-Iranian branch of the Indo-European family of languages. It is distantly related to Latin, Greek, the Romance, Slavic and Teutonic languages, and English. Kurdish, Baluchi, Pashtu and Osetic are the other modern Iranian languages.)

yavuzovic wrote: ↑

Sat Jan 23, 2021 5:35 pm

638 AD Jerusalem is captured by Arabian Empire. It must be one of the cities that changed it's ruler so many times.

(Farsi is a good language to learn because it is very close to other languages of the region. From internet: Persian is one of the most important members of the Indo-Iranian branch of the Indo-European family of languages. It is distantly related to Latin, Greek, the Romance, Slavic and Teutonic languages, and English. Kurdish, Baluchi, Pashtu and Osetic are the other modern Iranian languages.)

Yep

639 AD Arabs invade Egypt and capture Pelusium. They will soon take the whole of the country exterminating the ancient Egyptians transforming the country's population to what it is today.

640 acres in a square mile

641 AD Emperor Heraclius dies after 31 years on the throne (quite a long time for any king and especially for a medieval monarch).

PRINCE WILLIAM wrote: ↑

Sun Jan 24, 2021 10:18 am

641 AD Emperor Heraclius dies after 31 years on the throne (quite a long time for any king and especially for a medieval monarch).

His reign is around the average life expectancy isn't it?

That's right, at the time life expectancy, especially at the poorest social classes, was around 30 years.

642 King and saint Oswald of Northumbria is killed in battle on August the 5th. After the battle of Maserfield King Penda of Mercia orders the decapitation of the dead Oswald (there was a reason Penda was notorious).

Do not get confused between life expectancy and average age at death (especially for those reaching adulthood). Life expectancy for that era is highly affected by infant mortality and leads to such a low number which is commonly misinterpreted.

If half of births die before reaching their first birthday, a tiny minority die at about 30 and the rest die at 60, life expectancy would be about 30 but death at age 30 highly unusual.

Obviously this is extreme but illustrates how the life expectancy statistic in isolation can be highly misleading.