Knights and Knaves

 

The site with the 382 puzzles I mentioned is found here

The site that I downloaded SmoothDraw can be found here

Attribution for the images I have used:

Knave image: By GDuwen at English Wikipedia, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=6413428

Knight image: By Guilelmus Peraldus, Summa de virtutibus et vitiis – http://minos1.bl.uk/catalogues/illuminatedmanuscripts/ILLUMINBig.ASP?size=big&IllID=39600, Public Domain, https://commons.wikimedia.org/w/index.php?curid=11353133

Fractals

Fractals might be something that you have never heard of, even though fractals are objects that are observable in nature and can create beautiful art. So, what exactly are fractals? Fractals are objects or patterns that repeat an infinite amount of steps, each step being on a smaller scale. The easiest way to show this is by giving an example of a popular fractal known as the Sierpinski Gasket.

The Sierpinski Gasket

First, let’s start with a single triangle.

triangle_1

For the next step, we create a triangle by drawing lines between the midpoints of our original triangle. Then, carving the triangle out will result in a shape that looks like this.

triangle_2small

This process is repeated in the resulting three black triangles to create the next shape.

triangle_3

Repeat this process a few more times, and we end up with this.

triangle_4

Voilà! An intricate design created by doing a simple step multiple times. That is the beauty of fractals. The Sierpinski Gasket that I showed is just one of many fractals that exist. In fact, fractals can be created quite easily by computer programs. It is as simple as telling the program to repeat the same process over and over, each time on a smaller scale.

Want to create some fractals of your own? Try making one at scratch! At this site you can create fractals in seconds simply by drawing some lines.

Want to see fractals that appear in nature? Then please check out themindunleashed, where you can check out beautiful fractals such as snail shells and trees.

The possibilities are near endless when it comes to fractals. I hope you enjoyed the brief glimpse into the world of fractals that I have provided. If you have any fractals you would like to share, then please do so in the comments below!

Math art

There are few people who would associate mathematics with art. So it might come as a surprise to certain people that there are numerous pieces of art that are either influenced or fully constructed by mathematics. Please enjoy the links below, that lead to artworks of a few authors, and the gallery of math art.

Hiroshi Sugimoto

M. C. Escher

By Max Ronnersjö – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=19108050
http://www.paolouccello.org/Battle-of-San-Romano-(Battaglia-di-San-Romano).html | https://creativecommons.org/licenses/by-nc-nd/3.0/
CC BY 2.5, https://en.wikipedia.org/w/index.php?curid=8110428
By Tony Robbin – The uploader on Wikimedia Commons received this from the author/copyright holder., CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=2549880
https://archive.org/details/mathematics_84928305
https://archive.org/details/mathematics_70016004
By watz – http://www.flickr.com/photos/watz/1471094071/, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=4073914

 

Birthday Problem

In this post I will be explaining the Birthday Problem. The Birthday Problem asks what are the chances someone shares a birthday within a room. The results are not intuitive to what one would believe. Please let me know what you think about this problem and if there is anything of interest that you would like me to cover next!