## 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

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

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:

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