- The return of your second assignment:
- I was gentle this time (and on your first assignment) --
but I'm going to get tougher!
- Make sure that you type.
- On your writing:
- If I ask for paragraphs, give me paragraphs.
- I'm expecting complete sentences, correct spelling, correct grammar, etc.
- Err on the side of explaining too much, rather than too little.
- On the largest number you can make with your two hands:
- Humans have ten fingers, so we've ended up
with a decimal number system: but it wasn't
always so! With ten fingers we can represent
- 10
- 55
- 1023 (using binary, or base 2)
- 1,111,111,111
- infinity (but it's not a number)
- any number you want, using a typewriter!
- Some excellent responses
- What makes these responses excellent?
- Change the problem slightly: what's the
largest number that you can count up to on your
fingers?
That is, you must be able to take a static photo of your hands and be able to tell what number is indicated, and be able via this process to count from 0 up to that number by 1s.
- Humans have ten fingers, so we've ended up
with a decimal number system: but it wasn't
always so! With ten fingers we can represent
- On the number 1729:
- decimal representation: 1729 = 1 thousand, 7
hundreds, 2 tens, and 9 ones, or
- Ramanujan's representation:
- Those of you who calculated a mean made two
mistakes:
- "Grasping at straws" (you saw the mathematical word mean, in bold, and seized on it to compute an average of 1, 7, 2, and 9. Some of you thought that putting a mathematical word in bold was a hint. No!
- The second mistake was a mistake of the
English language: let's break down the sentence
What does each of the digits in the number 1729 mean? (The point of making the word "mean" bold is to emphasize it in speech: words are meant to be read, and we need to provide clues to readers as to how to read our words.)
The two prepositional phrases "in the number 1729" and "of the digits" are modifiers: "in the number 1729" tells us what digits we're talking about, and "of the digits" tells us what "each" refers to.
The core of the sentence is this:
What does each mean? You say "Each what?"; I say "Each digit." You say "Which digits?", and I say "digits in the number 1729."
In the end, however, you must answer the question
What does each mean?
- From Matt Yagle's paper: "The digits in the number might represent letters making a four letter word." Not a bad idea! See The ASCII code.
- decimal representation: 1729 = 1 thousand, 7
hundreds, 2 tens, and 9 ones, or
- I was gentle this time (and on your first assignment) --
but I'm going to get tougher!
- Your next assignment (to hand in) is due Tuesday.
- Recalling a visit from the Great Fraudini!
- How does the game work?
- Can you win at the game?
- Each of you will be part of a team of three, taking turns playing the roles of contestent, Fraudini, and someone to check the play.
- You should be able to do it every time!
- For your homework, you should read this bases
reference. Other bases are used constantly -- for example, in this web
page:
- This page uses HTML to control its appearance. For example, the
background color for this page is given by the command
<body bgcolor="#FFF8DC">
What does #FFF8DC have to do with color?
- What are some other bases that we use in our lives? Where?
- This page uses HTML to control its appearance. For example, the
background color for this page is given by the command
- Translating between bases
- Write 53 (base 10) in base 2
- Write 100101101 (base 2) in base 10
- One of my favorite early introductions to bases was Tom Lehrer's New Math.