• ## Math books for kids

I've always wondered about how to get more kids into mathematics. I've even thought about writing math books aimed at children. To do that I want to read the existing literature out there. Let's compile kids' books and resources about teaching math

8 replies omitted in this preview.

• >>38

customer!

39°
• http://worrydream.com/SimulationAsAPracticalTool/

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• >>40
>Mathematics, as currently taught, consists of the manipulation of abstract symbols. For most people, the level of abstraction makes math unpleasant or unusable as a practical tool for exploring the problems of their lives.
>The simulations represent the problem concretely, without abstractions; provide a broader context, allowing a deeper understanding of the situation
This is interesting. The way I always saw it was that abstraction is the means by which we make logical thought, and was therefore the most important takeaway from mathematics.
Certainly learning practical applications is necessary as well, but being able to abstract those applications means they can be applied to more (possibly completely unrelated) situations...

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• ## Is this a thing?

1 reply omitted in this preview.

• Paywalled.
Can someone with access to the article, summarize shat the trick is ?

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• >>26
"This alternate method for solving quadratic equations uses the fact that parabolas are symmetrical.

For example, in this parabola:

y = x^2 – 4x – 5

The two solutions when y = 0 are the symmetrical points r and s, where the parabola crosses the x-axis.

The midpoint, or average, of r and s is the axis of symmetry of the parabola. We want r + s = –b, which happens when the average of r and s is –b ÷ 2. In this example: 4 ÷ 2 = 2.

The two solutions to the quadratic equation will be the axis of symmetry plus or minus an unknown amount, which we’ll call u. In this example:

r = 2 – u and s = 2 + u

To find u, we want the product of r and s to be equal to c, which in this example is –5. Rewriting r and s in terms of u:

r × s = –5

(2 – u) × (2 + u) = –5

Solving that yields 22 – u2 = –5 or u2 = 9, so u = 3 works.

The two solutions to this quadratic equation are 2 – u and 2 + u, or –1 and 5. In other words, this parabola intersects the x-axis when x = –1 and x = 5."

28°
• >>28
>Solving that yields 22 – u2 = –5 or u2 = 9, so u = 3 works.
Solving that yields 22 – u^2 = –5 or u^2 = 9, so u = 3 works.

Sorry. Copy-and-paste mistake.

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• Ever since that other anonymous website made a major contribution to mathematics, I feel like we should be able to do it too. I vote that we work on the Riemann Hypothesis.

2 replies omitted in this preview.

• >>3
maybe not? but, you know that's a really hard problem, right?....
do you even know anything about math?

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• The g-ds never give mortals possible tasks. Otherwise, they would have done it themselves.

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• Shouldn't we opt for something simpler first? Like developing calculus without limits or infinities - and then use that for something trivial, like plotting trajectory of a planet moving under influence of a black hole? Of course, somewhere in between we'll need to develop new theory of gravity with our new, finite, calculus.

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• ## The square root of 2 is irrational

Let $x$ be a positive number such that $x^2 = 2$. Assume for the sake of contradiction that $x$ is rational. Then there exist coprime non-negative integers $a,b$, with $b \ne 0$, such that $x = \frac{a}{b}$. Then we have $2 = x^2 = \frac{a^2}{b^2}$, so $a^2 = 2b^2$. Since $2$ is prime and $2$ divides $a^2$, $2$ must divide $a$. Say $a = 2c$ for some integer $c$. Then $4c^2 = a^2 = 2b^2$, so $2c^2 = b^2$, and therefore $2$ divides $b$. But then $a$ and $b$ are not coprime, which is a contradiction. Therefore $x$ is irrational. QED
• Thank you for your wonderful contribution! Always love to see some real maths here.

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• ## For all e>0, there exists a d>0 such that...

• Did you know that you can use LaTeX on this website?

$forall \ \varepsilon > 0, \exists \delta > 0$ such that...
10°
• >>10
Although, not all things you'd expect are supported so I guess my forall symbol failed there.

Anyway, just type it like this.

%%%
some text $some latex$ more text
%%%

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• >>11
Of course, it doesn't work for post titles.

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• ## Hello!

I love math!

• I love math too!