Not a coffee maker

- Do you know what I got for my birthday from my wife?
- A coffee maker?
- Nope. Three line segments that measured 1, a, and b.
- How thoughtful of her. I guess you didn’t have them already.
- You are right. It made me extremely happy.
- How long did the happiness last?
- Till the next morning.
- What happened then?
- She asked me to make a line segment which measured a times b.
- I would have preferred the coffee maker.

Problem source: Pandalous.

9 Responses to “Not a coffee maker”

  1. Richard Sabey Says:

    Draw two intersecting lines L, M at random. Let them intersect at A. On line L construct B and C on opposite sides of A such that AB = a and AC = b. On line M construct D such that AD = 1. Construct the circle that goes through B, C and D. It intersects M at E where AE = ab.

    To construct the circle: construct the perpendicular bisectors of the line segments BC and CD. These intersect at O, the centre of the circle. The circle’s radius is OB.

    Cf:
    Intersecting Chords theorem

  2. Adam Says:

    @ Richard – thanks. lol – Can’t we just have the coffee instead?

    - Adam

  3. Jill Says:

    ha ha – kind of reminds me of René Magritte painting if a pipe with the inscription “This Is Not A Pipe” - Jill Copper

  4. Daniel Says:

    Who says the pyramids were built by extraterrestrials? Richard, I never would have thought of that…but I do follow your instructions of the theorem quite clearly.

    I’m sure, also, that you have forgotten more geometry than I will ever remember.

    Well done, sir.

  5. Anceps Says:

    It can be done quicklier using Thales’ Intercept Theorem:

    Thales_theorem_1.png

    A- – - -E- -C
    ¦
    ¦
    D
    ¦
    B

    If AD is 1, AB is b and AE is a,
    then, AC is ab!

    Using the Intersecting Chord Theorem would be far better for this problem:
    Given a segment of length 1 and another segment s, find a segment of length that is the square root of s.
    (Which is the same as using the right triangle altitude formula* and Thales’ Circle Theorem)

    *In a right triangle, the altitude with the hypotenuse as base divides the hypotenuse into two lengths p and q. If we denote the length of the altitude by h, we then have the relation h^2 = pq.

  6. Jesse Jelley Says:

    Wow, okay, you all went totally over my head! I guess I don’t remember my geometry from junior high. LOL! Either way, love coffee, not necessarily this machine. I def. drink too coffee to do one cup at a time. :)

  7. Jim Says:

    Well that formula would certainly give me a headache if I could not have my coffee first. Maybe you will get lucky on next years birthday!

  8. Truck Bodies Says:

    Why was this coffee machine worth mentioning in the first place? lol. I guess that’s just something you expected but, if she is the type of woman who does this instead…i just dont see the connection. Interesting story though.

  9. Brett Says:

    lol. a lot of these replays are hilarious!!

    Not a coffee machine? Well they tricked me :)

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