Overview

• You ask questions.
• I give long rambling answers.
• You ask for clarification.
• I attempt to clarify.
• We do it all over again (stopping when we run out of questions or out of time)

What should we submit for the labs?

• Your answers to the questions, fairly briefly.
  • Cut-and-paste code.
  • Type your reflection.

Why can't I get the image to show up on the reading for tomorrow?

• Ignore the error message at the bottom.
• Images don't show up until you use image-show.

What if I want to see the full circle?

(define d2 (hshift-drawing 50
                           (vshift-drawing 50 d1)))

What is this strange (provide (all-defined out)) incantation?

• Model: We have some definitions in one file and we're trying to use them in another file.
• Experience suggests that we only want to reveal some of those definitions to the the "client"
• (export ...) says which definitions get exported
• (export (all-defined out)) says "export everything I've defined; don't make me retype"

Extra 1 on yesterday's lab asks us to round a number to the hundredth place. How do we do that?

• I'd prefer not to give a full answer because it's on the homework.
• What might be helpful?
  • round (or truncate, or floor, or ceiling)
  • Would it be helpful to move the decimal place?

How can we see what's defined?

• The reference links should lead to useful references. (They don't always, so let me know when links are broken.)

Will you ask us some questions so that we can check our knowledge?

• Four mechanisms for dropping decimal portion: round, truncate, floor, and ceiling.
• When do round and truncate give the same value?
  
  • When the portion after the decimal point is below .5
• When do round and truncate give different values?
  • When the portion after the decimal point is .5 or above
  • Or is it the other way around?
• Observation:
  • Slightly different behavior for negative numbers
  • Also seemingly inconsistent behavior (round 2.5) -> 2.0 (round 3.5) -> 4.0
  • Is it that there is a hidden approximation?
    • Experiment suggests no
  • Further experiments: Rounds .5 toward even

• When do floor and truncate give the same value? When do floor and truncate give different values?

  • Think about it on your own

• Reminder: What are the key components of an algorithm?

  • Variables
    • Typing? You need to input information, and variables represent information
    • "today's eboard" names the random thoughts Sam is recording
  • Parameters
    • question - the input to the "Sam Rambles" algorithm
  • Conditionals
    • Student: If you understand, nod. If you don't understand, frown or ask for clarification.
  • Repetition
    • Repeat (Accept question, Give answer) until we run out of time.
  • Subroutine/Procedure
    • define in all of the Scheme code Sam typed
    • "answer question" encoded in Sam's head
    • "choose a student to call on"
    • "typing"
  • Sequencing
    • questions should normally come before answers
  • Some set of built-in operations
    • typing

• Fill in the following table

  val             -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
  (mod val 5)      2  3  4  0  1  2  3  4 0 1 2 3 4 0 1 2
  (rem.. val 5)   -3  -2 -1 0  -4 -3 -2 -1 0
  

• Why might you ever want the mod operation?

  • Maybe while we're counting, we also want to do some sort of cycle.

• How might you explain the mod operation to someone who didn't understand it?

  • "Math on a clock" - E.g., if there are five hours in a day, and Corey works for 7 hours and starts at 2, what time is Corey done?
  • For positive numbers, it's the same as the remainder.
    • For negative numbers, it's more complicated. (take the remainder and add the modulus/divisor)
  • On the negative side of the number line, the mod approaches the number from the right, the remainder from the left? (Sam did not phrase this well.)