now i understand why i was messing up my negatives and i liked the analogies the guy made
this is a good opportunity,help to me for my studies
I’m sorry, but I really don’t like your “debt” analogy of negative numbers, and here’s why.
From what I understand from the article, if I have one cow and then lend it to a friend, I have -1 cows. OK, that seems fair enough, but what if I start with 11 cows? I have 11 cows and lend 1 to a friend. By the analogy given, I would have 9 cows remaining. But any fool can look at my field and see 10 cows grazing, not 9.
Here’s an alternate analogy that I think makes more sense, still using cows and debt. Let’s say my friend has 10 cows and I have none, poor me. So I ask to borrow one of his cows, and I’ll give it back at the end of the week. I still have a net 0 cows in my field, because there’s one there, and a negative cow, that I need to give back. Everything is fine and dandy, until the cow dies. Now I have nothing but still owe someone something. The total balance is -1 cows.
I’ve made a website regarding the same topic in the Dutch language, that also contains many math topics and how to learn it the easy way. So for the Dutch visitors among you feel free to visit my website http://www.rekenvragen.nl/
Thos was a VERY GOOD passage about math and it helped me a lot in math class period THANK YOU SOOOOOOO MUCH for this passage !!! ####
As a college student studying mechanical engineering, math is taught accordingly at high school. I’m assuming the age group you are talking is between the ages of 12 and 17? In order to understand mathematics you need a strong background in geometry, algebra 1, 2, trigonometry, and others. In order to understand complex relationships regarding Pythagorean’s Theorem, negative numbers, derivatives, integrals, and graphs of all sorts you will need to have taken calc based physics 1 and preferably 2. Concepts in these classes would be too much to wrap their head around.
I just want to let you know that this was a good read! Just giving my opinion! 
@Sullivan: Thanks for the note!
@Micky: Glad you enjoyed it!
The pun "what does a sqrt(-17) cow look like?"made me laugh.
When we see a flying plane, a winning gambler, an exploding star, or a simple man walking, we try to back it up with numbers, equations, symbols etc. using a tool called Mathematics. Humans represent the facts of life (in observation and imagination) through Mathematics.
Science is about “forecasting on the basis of observation”. And so is Mathematics (although it’s not a science; it’s a prominent tool for scientists). In our quest of moving from ‘descriptive’ (what we observe) to ‘prescriptive’ (what we forecast) we end up imagining a lot. Zero, iota, fractions, negative numbers, higher than 3 dimensions etc., which is hard to visualize. But it does not make it wrong. We could be incapable of visualizing, Mathematics is not. The Mathematics from its basic building block has a very nature of being self-validating. Mathematics cannot be wrong. Thinking of 3 negative cows in place of 3 lent cows would be although meaningless, for Mathematics it makes sense. And in its quest of being ‘predictive’, this tool does its job very well. For example, if I were milking the cows everyday and selling milk to make money, during the days my cows were missing I was actually spending my old savings which accounts for the negative count of cows here. As I said, it does its job of ‘prediction’ really well. Mathematics takes into account the real variables from the world, and predicts the outcome in terms of real variables, however in the pathway of doing so it sometimes goes off the ‘observational world’ and takes a dive into imaginary (yet validated) concepts that one can only imagine.
If the problem statement would not just be about the lending cows but something more complex, we might even witness exponentiated and logarithmized cows, and in some really fancy problem, a sqrt(-17) cow, too.
vedic maths is a ancient indian mathematics, by using it mathematics can be practically understand for age group of 5to 15.
http://vmat.in
It good to know that someone cares about teaching Mathematics the right way.
Thank you
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Excellent site. Regarding negative cows, here’s a way to think about it: I have 3 cows and own three cows, while you have zero cows and own zero cows. I lend you my cows. Now I have zero cows and own three cows while you have 3 cows and own negative 3 cows. The negative cow does not represent what is owed to me from someone else, it represents what is owed to someone else from me, which is why negatives work with debt so nicely. The confusion comes from mixing the ownership with possession.
-R
Great analogy. Mixing possession/ownership makes a single scale confusing.