During this activity, it was very easy to determine what the trend was. When x = a negative number, the points on the y axis progressed very slowly, while once x = a positive number, it began to rise very quickly. I think it was a very good visual to understand negative exponents, and really get across that they are quite small.
The data table was also surprisingly helpful. It became much clearer to me that the difference between positive and negative exponents is that the main number (x) stays the same, but with a negative exponent, it’s the denominator.
The Golden Ratio is quite possibly the most common use of mathematics in the art world, and it’s completely irrational.
Let me explain.
The Golden Ratio is actually a number, typically written as the Greek symbol “phi” Φ. The number itself is about 1.6180339887… onward till infinity. Because of it’s non-repeating and non-terminating nature, it is considered an “irrational number”.
However, the use of the number is pretty rational, and incredibly logical, despite its frequent use in art. It dates all the way back to about 440 BCE, with the construction of the Parthenon statues, and the buildings of the Great Pyramids of Giza. These structures use the Golden Ratio, even if it wasn’t officially defined until at least a hundred years later, by the ancient Greek philosopher Euclid.
The Golden Ratio itself is used for perfect symmetry on the human body, in art, and architecture. It’s also related to the Fibonacci sequence, but you’d have to get a much more knowledgeable mathematician than myself to explain it.
It appears in a lot of famous works – Michelangelo’s David sculpture (used as an example of perfect human proportions), many of Leonardo Di Vinci’s works (including The Last Supper) and Salvador Dali’s The Sacrament of the Last Supper. (This piece of art also includes a dodecahedron – connections!) It also sometimes appears in nature, which is pretty cool.
Basically math has made its way into art and every other facet of life. So if you were going to pursue a career in the arts just to avoid math, bad move, buddy. Math is everything.
Sources: Art class from grade eight (ask M. Mackenzie), http://www.livescience.com/37704-phi-golden-ratio.html
Gum B (Big League Chew) proved to have the superior bubble blowing capabilities, thus disproving our hypothesis that Gum A would produce the largest bubble, due to its tougher consistency. Gum B’s bubbles were an average of 13.3 cm larger than Gum A’s, and the time needed to chew the hum to produce the bubble was significantly shorter than Gum A.
Our initial hypotheses stated that Gum A would prove to be the better gum, as it had a tougher dexterity/consistency than Gum B, and it was thought that this feature would help [the gum] sustain more pressure, such as air and physical stress, than its counterpart. However, this proved to be false as Gum B’s loose, powdery consistency turned out to be superior when it comes to blowing bubbles and stretching the gum itself.
The data we collected can be described as both qualitative and quantitative, as we measured the quality of the gum (how much stress the gum can sustain) and the quantity of volume of the blown bubbles (measured the area that each bubble takes up).
SI units were used in the lab (grams, seconds).
Five variables that my have affected the outcome of this experiment:
- Time spent chewing the gum.
- Contents of the saliva of the Chewer (based on what they ate, how many liquids have been consumed, etc..)
- Time the gum was exposed to the atmosphere of the lab (chewed Gum B was exposed for less time than Gum A)
- Faults in measuring (human error)
- Unknown amount of influence of the act of practicing blowing bubbles (the theory that the more bubbles blown, the bigger they will get)
The Test Subject (aka the Chewing Gum Inflation Device aka CGID aka Chloe)
- Explain your process.
- We analyzed the mental image of a soccer ball, and decided to create a series of pentagons that we would then attach to each other to make the sphere.
- We made a base of one pentagon, and then attempted to add five pentagons (one per side), taking a way the overlapping edges as we go along.
- This proved to be inefficient. The structure was not strong enough to stay up by itself, and we didn’t have enough time to resolve a problem with this prototype. So, upon realizing that combining and molding the marshmallows together we could make a ball, that’s what we did. We picked up the remaining marshmallows, rolled them together, and enforced the ball by putting in small pieces of raw spaghetti.
- What did you learn/change?
- We learned that our structure wasn’t stable or strong enough to stay up by itself, so we resolved that the next time we had to create a soccer ball out of marshmallows and raw spaghetti, we would reinforce each side of the pentagon with two layers of spaghetti instead of just one.
- As a direct result of this problem, we resolved that we would abandon our current prototype and instead form all the available marshmallows into a ball, thus creating a soccer ball. This was also due to lack of time available in creating the soccer ball.
- We learned that we are not the most experienced when it comes to creating spheres with the materials available, even though we have used them to make prisms since elementary school.
- How is this a math problem?
- It involves a lot of geometry, regarding the actual properties of a soccerball.
- Despite not actually doing any calculations, it’s probably a math problem. Anything is a math problem if you look hard enough.
After the video, we figured that our main problem lied in making the whole shape out of pentagons, while in reality, a soccer ball is made out of 12 pentagons and 20 hexagons.