I think it was Descartes who unified the two. Analytic geometry, or Cartesian geometry, plots the algebraic/geometric expression in a coordinate system of one, two or three dimensions. Doing that allows you to “plot” the results of your algebra on a graph, and do the reverse (extract.) Same when performing calculus. Basic mathematical analysis (senior high school and freshman college) has to have both calculus and analytic geometry.
Synthetic geometry (I learned that term just now) is your junior high geometry wherein you study axioms related to shapes to solve problems. This is pure geometry, the kind the Romans were good at. It’s a good discipline on its own, along with trigonometry, but I feel geometry really took off with the Cartesian system.
I think you mean the Greeks. The Romans were a lot more interested in applied math. They preferred building aqueducts and coliseums instead of arguing over lines in the sand.
Possible. Well geometry is a very useful tool in engineering. I’m still wondering why modern humans are so awed by things like the Nazca lines, when a competent surveyor in ancient times could have easily laid out those patterns with a measuring tape, a string, and a triangular template.
I said the Roman bit to contrast with the Arabs, who seemed to find algebra a bigger turn on.
Indeed. Skeptic Joe Nickell made a full-size replica of one of the Nazca figues over thirty years ago, using just basic equipment – strings and pegs. Here’s the article he wrote about it, with pictures:
One thing to be aware of is this isn’t really keeping Alg II, it wasn’t there 20 years ago and isn’t there for a lot of states now. Its been added under the Lake Woebegon Theory of Education that P-Man points out.
Most of that stuff is covered in Alg I: Khan Academy
Alg II takes that stuff and adds to it: Khan Academy
And the issue isn’t that its not ok to be bad at something, its that if you are bad at this, you don’t graduate high school. You can’t go on to trade school, you can’t go to community college, you are going to struggle to find a living wage job. The other thing that has happened in Lake Woebegon is that they’ve gotten hard assed on grades. Math isn’t subjective, where they can give you a few extra points on the essay to get you the D- you need to pass. Teachers don’t tend to give points for trying. Turning in all of your homework and getting 100% on it all is only worth 15% of a grade - 85% of the grade in my kids high school - and the other high schools my friend’s kids go to - is tests. A kid who is bad at math with test anxiety and undiagnosed ADHD now has a career running the french fry machine.
I took it junior year and failed the first semester; I managed to pull out a D- for the year. Junior year was when it was normally taken back in the dark ages. My kids took it in 8th and 10th; both aced it.
Because I knew I would hate it so I wanted to put it off as long as possible. I tried to get out of the requirement by taking it as a correspondence course but couldn’t even get up the motivation to make it past the first couple of chapters so I was stuck taking it the long way. I probably failed the class in reality but the teacher was not going to stop me from graduating and going to college. I took other classes from him as well and did fine in those. It was just that one.
That’s a large part of the reason why I don’t have a business degree - I thought it was going to be stuff like “How to run a business” and “How to lead people” and “Contract negotiations” and stuff like that. Instead, the first year was full of filthy, evil, Communist maths - none of which anyone was ever able to satisfactorily explain the relevance of.
35 years ago in high school I had algebra 1, 2, Geometry, Trig, Adv senior math, and programming. Aced them all. 3 years of college with Calc, Adv Calc, Business Math, and Statistics along with Logic. Mostly B’s. Went to work in industrial trades with some electrical engineering. Reading through this thread, most of the math terminology is foreign. I don’t remember hardly any of it. Most everything I need, I look up on a chart. If I need to know what formula to use, I look it up. Hard to explain to my two high schoolers why they have to know this stuff beyond because.
I believe that learning Algebra I teaches the student how to think Algebraically, to mean instead of solving 2 + 3 = ?, we solve 2 + ? = 5. This is an important way to think of things, what to we need to add to what we have to get to what we want, and this way of thinking is just one more tool in the students’ toolbox to manage all of life’s experiences.
In geometry, the student learns all them proof and derivations and this teaches the logical way to deduce answers. Again, just another tool in the students’ toolbox.
In a world full of trade offs, we need to balance each consideration, give each some weight and logically deduce which choice best serves our needs. This doesn’t seem like an Algebraic or geometric problem, but we can use these techniques to find our solution. My point is it’s hard to say whether we use Algebra on a regular basis or not. Certainly we’re not solving expanded polynomials, but how often to we use the techniques?
I agree Algebra II is overkill for most of the non-STEM fields, and replacing that class for statistics is an amazing good idea. In addition, I think a class that gives a quick survey of these “higher” mathematics would be great. Something where we just touch upon some of the concepts so that the student at least knows that there exists these “higher” techniques.
With STEM fields I think we do need to require these classes. I understand engineers just look up the information on a table, but making them take calculus works as a screening mechanism. Do we as a society want people who can’t pass college level mathematics designing our bridges, whether they use this math or not? That university degree is suppose to mean the holder has a universal education, they know something of calculus, chemistry, racial relationships, creative writing and a whole lot about 15th century French literature.
That’s the set-up for my funny tale … the teacher up front telling us to go ahead and forget everything we learned in those two years of high school Algebra … here’s the easy way to get the solutions … ten minutes later and I’ve basically never had to use Algebra again. Just too funny …
I have an accounting degree, so there is a huge need to be able to put the numbers in the right order to figure out future value or calculate straight line depreciation or run an ROI calculation or model variable costs.
But its mostly Alg I stuff. I’m sure financial derivatives take a lot more math.
I’ll be honest, I’ve done so much maths in my life that I kind of forget what I did when. Also, in sixth form (when you do the exams that get you into University) I also did Further Maths, which is a very optional extension of what’s in the national curriculum.
I do remember a lecturer saying that a large part of the first year at university was going to be repeating stuff I’d done at school as they need to cover everything so everyone would be at the same level.
Regarding what I use it for, I’m a computer programmer. I find a lot of the way I think stems from all the maths I did. In my day job I do a lot of database work - relational databases are based pretty much on set theory.
In my spare time a I write games. That can be very maths heavy, especially 3D stuff. And if you are interested in the behind the scenes stuff then it gets VERY maths heavy. For example, most 3D engines use quaternions instead of Euler angles to calculate rotations and movement in 3D space as doing so avoids the problem of gimbal lock (remember In old first person shooters how you couldn’t look directly up? That was an even simpler solution to the same problem).
