This is the fourth of our three WitCHes on VCAA’s Specialist Mathematics Exam 1 Sample Questions. Yeah, yeah it’s Douglas Adams-ish, but it wasn’t deliberate. We were undecided on this last one, and it’s not as compelling as the others. But, for similar reasons for the other WitCHes, we changed our mind and decided to post it. (There were other close calls, and we’ll soon update this post with brief comments on all the questions.)
Tag: irrational numbers
Well, WitCH 2, WitCH 3 and Tweel’s Mathematical Puzzle are still there to ponder. A reminder, it’s up to you, Dear Readers, to identify the crap. There’s so much crap, however, and so little time. So, it’s onwards and downwards we go.
Our new WitCH, courtesy of New Century Mathematics, Year 10 (2014), is inspired by the Evil Mathologer‘s latest video. The video and the accompanying articles took the Evil Mathologer (and his evil sidekick) hundreds of hours to complete. By comparison, one can ponder how many minutes were spent on the following diagram:
OK, Dear Readers, time to get to work. Grab yourself a coffee and see if you can itemise all that is wrong with the above.
Well done, craphunters. Here’s a summary, with a couple craps not raised in the comments below:
- In the ratio a/b, the nature of a and b is left unspecified.
- The disconnected bubbles within the diagram misleadingly suggest the existence of other, unspecified real numbers.
- The rational bubbles overlap, since any integer can also be represented as a terminating decimal and as a recurring decimal. For example, 1 = 1.0 = 0.999… (See here and here and here for semi-standard definitions.) Similarly, any terminating decimal can also be represented as a recurring decimal.
- A percentage need not be terminating, or even rational. For example, π% is a perfectly fine percentage.
- Whatever “surd” means, the listed examples suggest way too restrictive a definition. Even if surd is intended to refer to “all rooty things”, this will not include all algebraic numbers, which is what is required here.
- The expression “have no pattern and are non-recurring” is largely meaningless. To the extent it is meaningful it should be attached to all irrational numbers, not just transcendentals.
- The decimal examples of transcendentals are meaningless.