The new trend in album art is go geometric!! And is seems to be working...
Take a look at these albums in the top 100 on itunes!
Bruno Mars makes a bold attempt, but someone needs to remind him it is impossible to cover the surface of a sphere with perfect squares!! A sphere is not a Euclidean surface, the sum of the angles in a quadrilateral exceeds 360. Maybe you need to review your spherical geometry notes, Bruno.
Jason Mraz joins the game using geometric figures rather than letters. Will this catch on? Can we abolish the alphabet? Although the E is a bit shaky, I think we all know what he is trying to say. Jason loves his Geometry. I'm sure this warms his math teachers' hearts.
Although only #86 on itunes, Gotye's Somebody that I used to know may be my favorite cover.
Notice the Geometry and shading. Four equal squares are crisscrossed by a number of diagonals. There is some rotational symmetry about the center and for those of you who are more advanced, you may notice a glide rotation!! Clearly marketing to the Math geeks!!
Cher Lloyd and Calvin Harris deserve a mention. Check out their covers to see if you can recognize the geometry yourself. Who knows, maybe they will be trending up in the week to come.
One of the natural wonders of the world is the Giant's Causeway in Northern Ireland. It is a natural rock formation that extends from the north coast of the island into the North Sea, continuing under the sea all the way to Scotland. Legend claims that this is the route that giants used to travel between the islands.
It is truly amazing that the stone pillars formed the way they did.
They are hexagonal prisms, just like the ones you heard about in Geometry class, but never thought existed.
Imagine Dragons has slightly altered the natural landscape to form pentagonal prisms on their debut album, night visions. I wonder what happened to the sixth lateral face? Do you suppose the dragons chased it away? And where are the giants? Imagine...
This website will allow you to make a net to create your own hexagonal prism or just manipulate one to see it from all sides.
http://mathworld.wolfram.com/HexagonalPrism.html
Those of you who have been studying the Cartesian Coordinate system for years might feel a bit uncomfortable leaving the realm of (x,y) and entering the space of (r, theta). I have found some things that might make you feel more comfortable, or at least a little less wary.
Remember those childhood days you spent at the playground, swinging,
sliding and climbing on those rope ladders? You may have thought those
ropes were supposed to look like spider web, but in fact they were simply preparing you for your high school math class, when you entered the polar coordinate system. Just look at all those radii and angles. Now do you feel better?
Alternatively, you can imagine a red face plastered behind the circles and spokes. If Spidey has embraced it, so can you!!!
Use this link to play around with functions in polar coordinates. www.shodor.org/interactivate/activities/PolarCoordinates/
Input a function and then click on the plot/update button to see what the graph looks like or create a table of coordinate points. Try a variety of sine, cosine and tangent functions, such as sin(2*t), tan(4*t), cos(0.3*t). Try inputting large values (>100) for theta maximum and see what happens to your graphs. What do you notice? Why do you think this happens?
We all know about the gaggle of geese, the pod of whales, the pride of lions and the pack of wolves. But what on earth do you call a set of parallel lines?
I'll give you a hint. The guys from fun have used some for a colorful backdrop. The proper term for a group of parallel lines is a pencil of lines. In fact, a pencil is a family of geometric objects with a common property, for example the set of lines that are parallel. Just think of the pencils in the background.
A pencil of planes, the family of planes through a given straight line, is sometimes referred to as a fan. In the image on the left, the 3 planes belong to the pencil of planes that pass through a line of intersection.
Look at the shape of the icy cave entrance melted by the pounding surf or this double rainbow.
Have you seen a parabola lately? We can find some nearly perfect parabolas in nature. This stone arch is another prime example of a parabola formed by nature.
Parabolas are easy to create, just cut a slice out of an infinite cone and check out the infinite cross-section. Be careful, you have to slice at the correct angle, otherwise you might accidentally create a circle or an ellipse.
To create your own conic section check out this website: http://academic.sun.ac.za/mathed/shoma/Index14.htm
Perhaps an easier way to form a parabola is to suspend a shiny chain, holding one end in each of your hands. If you hang it in front of a black background, you may be able to reproduce the image that 2 Chainz created on this CD cover for Based on a T.R.U. Story.
These might even qualify as parallel parabolas. ;)
Looks like Flo Rida is quite proud of his single parabola.
http://www.billboard.com/images/pref_images/q00120e8szk.jpg
Keep your eyes open to find more parabolas around you.
To make your own parabolas and learn more about them, click on this link: www.mathwarehouse.com/quadratic/parabola/interactive-parabola.php
Bruno Mars makes a bold attempt, but someone needs to remind him it is impossible to cover the surface of a sphere with perfect squares!! A sphere is not a Euclidean surface, the sum of the angles in a quadrilateral exceeds 360. Maybe you need to review your spherical geometry notes, Bruno.
