Something I find really fascinating about rosettes is that they, like many mathematical shapes, can be found in nature. A great example of that is the difference between jaguars and leopards. Aside from the physical differences in the builds of the cats, with jaguars being stockier and slightly larger overall, their markings are different kinds of rosettes.
As you can see with this jaguar, its body is covered in black rosettes over a golden-tan coat for camouflage. Said rosettes are comprised of dots forming a circle, within which there is always at least one dot, sometimes more.
As you can see with this leopard, it also has black rosettes over a golden-tan coat, but its rosettes are smaller, but, more importantly, comprised of circles of dots, without anything in the center. Being able to see the differences in these rosettes is very helpful in distinguishing between these two species, and being able to spot natural rosettes and other kinds of designs can be helpful in distinguishing differences between numerous species, all over the world.
I know a lot of people don’t like spiders, but with the most recent conversation of symmetry we had in class, I can finally talk about them, and even show a picture of one! I specifically picked a very large species, shown below, which is the Giant Huntsman Spider, so called because they can reach a leg span of 12 inches, and they don’t make webs, but chase down (hunt) their prey. Aside from the incredible importance spiders have in keeping pest insect populations down, they are also symmetrical, as can be seen below.
Not only are they symmetrical, but they are also not chiral; their reflections would look exactly the same, and their original images could be superimposed on the mirror ones. This perspective gives the spider a kind of beauty, in my eyes. So, in conclusion, it’s amazing how many cases of natural symmetry can be found, and yay, for something finally giving me a reason to post and talk about the Giant Huntsman Spider!
In regards to the Four Color Theorem, I found it extremely interesting and, honestly, really cool that, in this case, adding more pieces to a puzzle doesn’t always mean that there will be more required to solve it. In fact, in most cases that we did in class, I found that the more pieces we added to the puzzle, the less colors we needed to put in. In the end, the best way to require the most colors was to think our way through the puzzles and put the pieces in certain arrangements, not adding in more.
I’ve always been taught, at least in science, that nothing can ever actually be proven possible or impossible. It can only have or lack support in its viability. However, it seems that in the world of mathematics, that’s not always the case. Things can in fact be proven possible or impossible, and there are new theories being created constantly that can do just that. That thought occurred to me when we went over Graph Theory, and were able to mathematically prove that the Seven Bridges of Konigsberg was an unsolvable problem. The fact that we could not only prove it was impossible, but also do it so simply and easily in a graph, was astounding. I’m still a biology major, and cells and microscopic organisms are still my greatest interest, but being able to 100% prove or disprove something will always be fascinating to me.
I find it interesting that there are different rates for paying taxes based on how much someone makes. It kind of seems like a sort of penalty for people who have a higher annual income. The taxes paid by someone who makes $100,000 a year are three times what someone who makes half of that pays! Maybe it would make more sense for there to just be a flat percentage of income everyone pays, regardless of what’s made? Of course, there’d be considerations for people with dependents and such, as there already are, but I’m wondering if that would work better? Maybe if that was applied to people who made more than, say, $15,000 to $18,000 a year?
There is a fine line between numerator and denominator, and only a fraction of people will get this joke… Some people appreciate it, others don’t, and the division is clear.