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Great Bedtime Puzzle

Here’s the puzzle a friend threw out:
triangle - geometry maths puzzle

My mathematics is so rusty (and even at its best, has never been any good) that it took me 3 hours to kill this and get to bed at last. Also, not even sure this attempt is right but it is definitely horrendously inelegant – my math teacher would have smacked me for this (and no, i have not double-checked my working for silly mistakes) but oh well, for the record:

geometry maths puzzle

Let ∠FBC be 20°.
=> ∠CFB = 80°

Since ∠BCF = ∠CFB. △BCF is isosceles.

Oh and also ∠CEB = 50°
(△ACB = 180° = 20° + 30° + 50 ° + 60° + ∠DBE => ∠DBE = 20°.
△BEC = 180° = 50° + 60° + 20° + ∠CEB => ∠CEB = 50°)
=> △BEC is also isosceles
=> BC = BF = BE
=> △BEF is “isosceles”

But wait, since ∠EBF = 60°, and △BEF is “isosceles”,
=> ∠BEF = ∠BFE = 120°/2 = 60°
=> △BEF is actually equilateral

∠DFE = 180°- 80°- 60° = 40°
∠BDF = 40°
(△BDF = 180° = 40° + 60° + 40° + ∠BDF => ∠BDF = 40°)

Since ∠BDF = ∠DBF = 40°,
=> △BDF is yet another isosceles
=> FD = FE = FB

But it is a happy penultimate one because
=> a last isosceles △FDE
=> ∠BDE = 30°
(∠DEF = ∠FDE = (180° – 40°)/2 = 70°
∠BDE = 70° – 40° = 30°)

Mathematics is exceeding beautiful – or rather, the consistency in this world observed and communicated by mathematical theorems is incredible. Yet it boggles the mind to realise that complex as mathematics can be, it doesn’t come close to comprehensively explaining the known creation. Even if one adds all the knowledge of physics and chemistry and biology, we have hardly scratched the surface of creation, much less understood anything about the purpose of it all or where it is going.

And how can one accept the usual throwaway line that science has proved that there isn’t a God? For that is to attribute to science (or mathematics) something that it does not claim – an understanding of the ultimate purpose of things, which in turn requires a Purposer of Things.

“But things could just exist without need for purpose or Purposer, or Creator.” That is no better a theory than that of the existence of an uncreated Purposer and Creator. And just on that point alone, the probability of a God who has made this world constant and mostly predictable, thus enabling such things as mathematics and science, is far higher.

But of course there is much more historical evidence that puts the whole thing way beyond reasonable doubt.

In other Things-With-Three-Parts news, here are some three-ingredient brownies I made for the poor catering people as they went into a whole week of cooking for A Passion For Life:
Nutella Cupcakes
Nutella (280g)
2 medium eggs
self-raising flour (62g)

1. Beat eggs.
2. Mix rest of stuff into beaten eggs.
3. Pour into muffin tins.
4. Bake at 180°C for around 30 minutes.
5. Ice with more Nutella and top with toasted hazelnuts.

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