Mathematics
Commutativity
A binary operation is said to commute if the order of the operands does not alter the result. In the real numbers, , the following commutative laws hold : for all for all Although these [more…]
OldTrout
Mathematics
Going Round in Circles
Or : Multiplying by . The beginning of complex numbers is often attributed to Cardano (1501 – 1576). Complex numbers provide a solution to the equation . They are an extension of the number system [more…]
Fascism
Letter From Tommy August 2019
Transcribed from Danny Tommo’s twitter feed, 2nd August. Well, here we are, it’s 5:30 PM, I wanted to wait until I had some updates before I put pen to paper. I’m receiving your emails [more…]
Mathematics
Two Squares and Four Squares
Diophantus of Alexandria wrote a collection of books called Arithmetica in the 3rd century AD. He noted that natural numbers of the form cannot be expressed as the sum of two square numbers. He also [more…]
Engineering
How about sending me a fourth gimbal for Christmas?
Part of a conversation between Mission Control and Apollo 11 : 104:59:27 Garriott: Columbia, Houston. Over. 104:59:34 Collins: Columbia. Go. 104:59:35 Garriott: Columbia, Houston. We noticed you are maneuvering very close to gimbal lock. I [more…]
Conservatives
Goodbye and Good Riddance
Haikus from the Gate Hangs High : Theresa’s treason: Treachery on Albion. Eat hungry gallows! Ang Ryman Vapid and inept Soulless and empty speeches Time to dance away Northern Man Abysmal failure [more…]
Mathematics
Heads, Tails And Beans |S|=6
This is an unintentional detour for our little course. I didn’t plan to investigate the factorial function in so much detail, but it came about quite by accident (or stupidity) as we’ll see in later [more…]
Mathematics
Heads, Tails And Beans |S|=5
Here we’ll look at some more probability calculations before moving on to permutations, combinations and the binomial theorem. More Probability… If you recall from the last part, we used set notation to describe a general [more…]
Mathematics
Heads, Tails And Beans |S|=4
So far, we’ve looked at sets and how they contain information that we wish to count in some way. How the power set \(\wp(S)\) can count all of the possible sub-sets of a given set [more…]