Welcome to math helper,
Personally, I think that the question 'Is math invented or
discovered?' is meaningless. But thinking about _why_ it's meaningless
can lead you to some very interesting ideas about the nature of
meaning!
(For example, if you're lucky it might lead you to read Doug
Hofstadter's wonderful essay 'A Conversation with Einstein's Brain',
in his book _The Mind's I_.) examples on math help; So I hope you'll continue to noodle
around with this issue this even after your essay has been completed.
I hope the above explanation was useful, now let us learn more on online math tutors.
Tuesday, August 17, 2010
Wednesday, August 11, 2010
math intuition
Welcome to free math tutor online,
One way to train my intuition is to compare the problem with something
I've seen plenty of times in real life. I've painted murals, mixing
the colors I want from poster paint. Often I want a light color, and a
little color goes a long way.
I have learned to be very careful not to
add too much color to the white at first. Why? I If I need 1 part blue
to 100 parts white (which is not unreasonable in my experience), and I
put in 2 dabs of blue instead of 1, meet math tutors online for more examples;
I need to add another 100 parts of
white to get the color to be what I wanted!
I can't tell you how many
times I've ended up with far more paint than I needed, by the time I
got the color right. I've learned that it's better to throw away half
the too-dark mixture, rather than try to save the whole batch by
adding white. learn more on math forum.
One way to train my intuition is to compare the problem with something
I've seen plenty of times in real life. I've painted murals, mixing
the colors I want from poster paint. Often I want a light color, and a
little color goes a long way.
I have learned to be very careful not to
add too much color to the white at first. Why? I If I need 1 part blue
to 100 parts white (which is not unreasonable in my experience), and I
put in 2 dabs of blue instead of 1, meet math tutors online for more examples;
I need to add another 100 parts of
white to get the color to be what I wanted!
I can't tell you how many
times I've ended up with far more paint than I needed, by the time I
got the color right. I've learned that it's better to throw away half
the too-dark mixture, rather than try to save the whole batch by
adding white. learn more on math forum.
Sphere of radius
Welcome to free online math tutoring,
We have a sphere of radius R, with a rope of length 2 pi R around its
circumference; then we add L units to that circumference. What is the
new radius of the rope? The new circumference is (2 pi R + L); the new
radius is that divided by 2 pi, or R + L/(2 pi). This means that the
radius is increased by L/(2 pi), which is independent of R.
This seems a little less surprising, perhaps, than if we solved it with specific
numbers, since we don't have a specific unexpectedly large number to
reject outright; we're forced to look at the algebra. more help on online math forum;
But we can still question the algebra once we see what it tells us.
The next step, of course, is to check the answer: plug in actual numbers for R and L,
solve for the change in R, and then add that to R to find what the new
circumference will be. It will be L more than the original, showing
that as long as we accept 2 pi R, our answer is right. read more on math forum.
We have a sphere of radius R, with a rope of length 2 pi R around its
circumference; then we add L units to that circumference. What is the
new radius of the rope? The new circumference is (2 pi R + L); the new
radius is that divided by 2 pi, or R + L/(2 pi). This means that the
radius is increased by L/(2 pi), which is independent of R.
This seems a little less surprising, perhaps, than if we solved it with specific
numbers, since we don't have a specific unexpectedly large number to
reject outright; we're forced to look at the algebra. more help on online math forum;
But we can still question the algebra once we see what it tells us.
The next step, of course, is to check the answer: plug in actual numbers for R and L,
solve for the change in R, and then add that to R to find what the new
circumference will be. It will be L more than the original, showing
that as long as we accept 2 pi R, our answer is right. read more on math forum.
Mathematics intuition
Welcome to free math tutoring online,
The first thing we have to recognize is that our intuition can be
wrong. Mathematicians (and the rest of us) need a healthy dose of
humility, because this happens all the time.
I suppose one of the
benefits of studying math beyond mere arithmetic is that it can teach
us not to trust our assumptions, or even what seems like sound
reasoning, but to look closely at the logic behind what we believe.
examples on online math forum; What seems true, not only in math
but in all of life, may not be! That's just part of growing up.
continue learning on our math forum.
The first thing we have to recognize is that our intuition can be
wrong. Mathematicians (and the rest of us) need a healthy dose of
humility, because this happens all the time.
I suppose one of the
benefits of studying math beyond mere arithmetic is that it can teach
us not to trust our assumptions, or even what seems like sound
reasoning, but to look closely at the logic behind what we believe.
examples on online math forum; What seems true, not only in math
but in all of life, may not be! That's just part of growing up.
continue learning on our math forum.
Math quadratic formula
Welcome to free math,
The quadratic formula,
-b +/- sqrt(b^2 - 4ac)
x = -----------------------
2a
applies whenever you have an equation like
ax^2 + bx + c = 0
So we can start with either the formula, or the equation. visit online math forum; Frankly, the
equation looks as if it will be less work:
ax^2 + bx + c = 0
bx = -ax^2 - c
b = (-ax^2 - c) / x
more exercise on math forum.
The quadratic formula,
-b +/- sqrt(b^2 - 4ac)
x = -----------------------
2a
applies whenever you have an equation like
ax^2 + bx + c = 0
So we can start with either the formula, or the equation. visit online math forum; Frankly, the
equation looks as if it will be less work:
ax^2 + bx + c = 0
bx = -ax^2 - c
b = (-ax^2 - c) / x
more exercise on math forum.
Subscribe to:
Posts (Atom)