Alright, new possible topic: “Why do people way-overprice things on ebay and Amazon?”
(Cuz one out of 6 billion just might bite. )
Hey, found my book! We have this shelf full of not-wide books, and this one was one of the “behind” books.
Mail it to the Lobsta
I could do that.
I believe that some luxury cars actually have comparatively low lease rates because they hold their value so well. Roughly the same lease rate for a $100K car that drops to $80k, and a $30k car that drops to $10k.
ISWYDT
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Golden ratio is actually very interesting due to the fibonacci numbers link, and how you can show how math is represented in nature via symmetry, but it will be very time consuming to study and then produce the required lessons.
Perhaps do something along the lines of “limits” and use the Golden Ratio (limit of the ratio of a Fibonacci number over its predecessor) and the Natural number (lim_{n\rightarrow\infty}(1+\frac1n)^n) as some interesting results. Then use some various “infinite” sequences that evaluate to \pi.
There is plenty of material in interest theory to make this interesting. If these are typical HS students you don’t want to go too deep.
If you want an idea a little outside of the usual you could do a business math payoff case with probabilities like 20% high success (maybe 100% payoff) 60% average (maybe 30% payoff) and 20% failure (maybe 50% loss) and PV that.
There is also “The Great Left-Handed Mortality Scare of 1991.”
Or, any of the topics in the Book “Innumeracy.”
I don’t think it works that way. Depreciation is not the only factor in lease cost.
It is a major factor.
Then, there is simple market demand.
There is the cost of owning a car that someone else is currently driving; contingencies and such.
There is the variation of wear and tear. Some dealers include free maintenance with a lease, so people don’t bring a car back with 30,000-mile-old oil.
Etc.
SL did not say it was the only factor. You inferred that SL thought it was the only factor. Shame on you. SHAME!! (-- Lincoln Electric)
I am talking about the interest owed on a larger borrowing amount.
If the lease interest rate was 0%, then 130K->110K would have the same payment as 30K->10K. If the interest rate were 10%, the extra $100K borrowed makes up the lease cost higher. It is only roughly the same for short lease periods and low interest rates.
Capstone project concept just got declined. Thats the last time i listen to you folks!
They rejected interest rate theory?
FTR, which project concept specifically was declined?
It’s apparently not outside the current curriculum, maybe not advanced enough. Interest rate theory.
I guess I better start learning about the golden ratio.
Switched and did a new proposal on diophantine equations. Reviewer said it was a great subject. If interest theory was going to be easy and the golden ratio difficult, and interest theory kind of boring and the golden ratio interesting, I guess diophantine equations is right in the middle. I’ll have to do some reading but I’m not starting from scratch. And it’s a reasonably interesting subject for me.
Guess I get started tonite!
Anyone have any interesting ideas on the topic other than say primes and pythagorean triples?
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Fermat’s Last Theorem is one of the most famous examples of a Diophantine equation.
But you could look at some questions of interest that would (eventually) lead to seeing Pythagorean triples as being part of a solution.
For example, consider the general equation for a circle: (x-h)^2+(y-k)^2=m.
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Start with the circle centered at the origin, and ask what is the smallest value of m that is needed to get have at least one non-trivial integer solution.
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Pick an appropriate number for m where the circle centered at the origin doesn’t have a Diophantine solution; then ask if there are values for h and k that can be used to result in a Diophantine solution. You could start with first picking a Pythagorean triple where the two smaller numbers are a bit larger, then you could “split” them to the above form.
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Aside:
Fun way to create Pythagorean Triples.
- Start with an odd number > 1, as one leg of a right triangle.
- Square it.
- Divide by 2.
- Round up = hypotenuse.
- Round down = other leg.
Try it!
3, 4, 5
5, 12, 13
7, 24, 25
9, 40, 41
etc.
Why?
A^2 + ((A^2 - 1)/2)^2 =
A^2 + (A^4 - 2A^2 + 1) / 4 =
4(A^2)/4 + (A^4 - 2A^2 + 1) / 4 =
(A^4 + 2A^2 + 1) / 4 =
((A^2 + 1) / 2)^2
What about even starting numbers? What about {8, 15, 17}?
I leave that as an exercise for the reader. (8^2 /2 = 32. Hey, 15+17= 32! Coincidence?)