Guilloché pattern and other Web apps

Here is nice Guilloché pattern generator done as web app. These patterns have long history and were used as ornaments by crafters. Wikipedia article about Guilloché is here.

The site has plenty interesting information about geometry, patterns, etc. For exampe a Butterfly curves web application.

Multiplication with your fingers

Here is interesting trick to multiply numbers in second half of multiplcation table (6-10). I do not recall where I learned it from but it has been around for quite some time. Best way to explain how it works is on example:

to multiply 6 by 7 you open 1 finger on one hand (6-5 = 1) and 2 fingers on another (7-5 = 2), then you multiply number of closed fingers on your hands and add it to sum of open fingers multiplied by 10. In our case -

4 (closed fingers on one hand) x 3 (closed fingers on another hand) + (1 + 2) * 10 = 42

another example:

8*9 translates to : 2*1 + (3+4) * 10 = 72

:)

Red-Black balls

Here is puzzle I heard on some radio or podcast show:

You are in the forest. Two trees are marked in some way. You are given rope which length is twice the distance between marked trees. The task is to find third tree that forms right triangle (triangle that has one angle of 90 degree).

There are few possible solutions here.

Relativity

Here is interesting question, while it's simple for people familiar with theory of relativity, imagining the followed experiment can be an eye openinig experience,

Imagine following device, the laser pointed straight up with a mirror mounted some distance above it that bounces light back to the laser where receptive is attached sensor. Knowing distance of round trip and time between sending light impulse and receiving it we can verify speed of light. Now lets place that device on very fast moving train. For the observer on the train nothing changes same data, same result. However for observer on the ground light now travels along zigzag or two sides of triangle covering more distance then in stationary case. Given that speed of light is the same in both cases, how is that possible?

Encyclopedia of Integer Sequences

The On-Line Encyclopedia of Integer Sequences is free searchable library of various integer sequences. While site is mostly dry and blant from UI point of view, it’s content that is most fastinating. You can search for various sequences and results can be represented as graphs or sounds and include links to relevant literature. Seraching for numbers from previous quiz will reveal the sequence

(I normally do not give away answers unless there is a post solving the puzzle. But in thi particular case the gIven sequence in the previous post is very hard to solve, still you can try solving it yourself and then look it up in encyclopedia).

Number sequences

Back from the break, with new interesting sequence I learned:

1 2 4 6 3 9 12 8 10 5…
what are the next number(s)?

This can be rather hard sequence to solve, it seems random but its actually not.

Beer Bubbles

Did you noticed that bubbles in the glass of beer or sparkling wine are moving down initially? It is true - just carefully watch the glass as you pour liquid in, people often do not notice small things like that. It seems counter intuitive, but explanation is rather simple. What is it ?

KaleidoTile

Jeff Weeks from geometrygames.org has released Mac OS X version of KaleidoTile. Learn about polyhedra and tilings while creating colorful kinematic art. The application has colorfull and easy to use interface which allows you to manipulate and animate various parameters in intuitive way. If you have 3D stereo glasses you can view object in 3D space. KaleidoTile is very nicely done little app, its free under GPL. Check it out!

Race

Mark and Steve ran 100 meter race and Mark won, he crossed finish line when Steve was at 95 meter mark. On second race Mark started 5 meters before starting line, so he was handicapped by the exact disatnce he won first race by. Given that speed both men is the same as it was in first race who will win second race ?

Two candles

Here is simple one, you have two candles of different length. You light both of them and cover them with glass cover of some sort (doesn't really matter what the cover is). Which one will die out first, tall candle or short one? It's easy to just do this experiment and and see it on practice, however thinking about what will happen is interesting and can lead astray.
Let us know what you think!
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Note: Comments may have spoilers! Come up with solution on your own before reading them.