16
votes
Imbuing a six year old with a sense of mathematical wonder
I remember being excited about the following at a young age.
If you add consecutive numbers you get triangle numbers.
Triangle numbers are fun.
If you put two consecutive triangle numbers together ...
- 7,999
15
votes
Imbuing a six year old with a sense of mathematical wonder
How about:
Numbers go the other way, too (negative)
You can cut numbers in half, forever
What if you cut a number into three pieces?
1 million is a thousand thousands (100 is ten tens)
If you don't ...
- 251
15
votes
Mnemonics for some properties in mathematics
Recently, a student in my beginning algebra course offered the following to the class, regarding signed number multiplication:
Assuming positivity is like love, and negativity is like hate, then...
"...
- 9,184
11
votes
Mnemonics for some properties in mathematics
The minimax theorem states the following:
Let $X\subset \mathbb{R}^{n}$ and $Y\subset \mathbb {R} ^{m}$ be
compact convex sets. If $ f:X\times Y\rightarrow \mathbb {R} $ is a
continuous ...
- 712
11
votes
Mnemonics for some properties in mathematics
I tell students to visualize $<$ and $>$ as mouths. They always want to eat the bigger number.
- 24.4k
10
votes
Mnemonics for some properties in mathematics
Fatou's Lemma states: for nonnegative measurable functions $f_n$,
$$
\int_E \liminf_{n\to\infty} f_n\;d\mu
\le
\liminf_{n \to \infty}\int_E f_n\;d\mu
$$
The mnemonic is
$$
\text{ILLLLLI},
$$
meaning "...
- 7,369
10
votes
Pi Day is approaching: What are some interesting math questions whose answer is exactly $\pi$?
Regarding your second example. Not only $\int_{-\infty}^\infty \frac{\sin x}{x} dx = \pi$, but also
$$\int_{-\infty}^\infty \frac{\sin x}{x} \frac{\sin (x/3)}{x/3} dx = \pi $$
$$\int_{-\infty}^\infty \...
- 201
7
votes
Imbuing a six year old with a sense of mathematical wonder
There is a great old Disney short called Donald Duck in Mathmagic Land.
As well as being delightfully drawn in the traditional Disney style, it contains lots of useful and occasionally surprising ...
- 71
6
votes
Entertaining and fun books about mathematics for (basically) liberal arts students
I'll suggest the book Flatland by Edwin A. Abbott. It's an interesting read about geometry and thinking in a higher dimension.
The downside is that this book is, well, antiquated to put it nicely. ...
- 4,606
6
votes
Imbuing a six year old with a sense of mathematical wonder
Below are some great and inspiring books by an excellent mathematician. (In the Really Big Numbers book, on the page where counting by tens is discussed there is an inspiring error (?)…Big Bird is ...
- 6,133
6
votes
Imbuing a six year old with a sense of mathematical wonder
The earlier question, "Teaching a very enthusiastic and bright 5 year old" could help.
Building and manipulating shapes enhances geometric imagination. Consider
polydrons, or
snap-cubes:
...
- 29.5k
6
votes
Pi Day is approaching: What are some interesting math questions whose answer is exactly $\pi$?
https://en.wikipedia.org/wiki/Buffon%27s_needle_problem
17 matches thrown randomly. Spacing between lines is 1 match length. 11 cross a line. $\frac{2 \cdot 17}{11} \approx 3.1 \approx \pi$.
- 24.4k
5
votes
Imbuing a six year old with a sense of mathematical wonder
Another book, to add to @Jon Bannon's list, that my 4 year old daughter and I can recommend is
Introductory Calculus For Infants. We also seem to discuss Graham's number a bit after watching the ...
- 151
5
votes
Imbuing a six year old with a sense of mathematical wonder
Arranging counters into groups (multiplication and division), so arranging 12 counters into 6x2, 3x4 etc, and realising that there are some numbers that cant' be arranged, no matter how hard you try (...
- 151
5
votes
Pi Day is approaching: What are some interesting math questions whose answer is exactly $\pi$?
"What are some interesting math questions whose answer is exactly $\pi$?"
The area of a unit circle--It is exactly $\pi$.
The proof is very neat and visual and can be understood by any ...
- 257
4
votes
Imbuing a six year old with a sense of mathematical wonder
Just to complete the list of books. Some time ago I read The Number Devil and liked very much. I think it is the proper book for your needs as the argument shows how a "math devil" shows math concepts ...
4
votes
Entertaining and fun books about mathematics for (basically) liberal arts students
The Number Devil: A Mathematical Journey by Hans Magnus Enzensberger is an essential in the "fun math book" category. Very accessible, great illustrations and actually touches on pretty sophisticated ...
- 5,030
4
votes
Mnemonics for some properties in mathematics
One I recently learned -- for the order of the signs in factoring a sum or difference of cubes, remember SOAP: Same sign, Opposite sign, Always a Plus.
Sum of Cubes: $x^3 + a^3 = (x + a)(x^2 - ax + a^...
- 24.4k
4
votes
Mnemonics for some properties in mathematics
This only makes sense in Spanish but it's pretty fun. For integration by parts,
$$
\int u dv = u v - \int v du
$$
Si un día vi una vaca menos sexy vestida de uniforme
Which translates roughly to:
...
- 336
4
votes
Is Calculus Made Easy by Silvanus P. Thompson a good book for first-time calculus learners?
After giving the book another look I have to expand on my comment above and make it stronger: no, this isn't a good book for a first-time learner, and in fact I think it's a terrible choice. I looked ...
- 1,527
4
votes
Is Calculus Made Easy by Silvanus P. Thompson a good book for first-time calculus learners?
The fact that the book uses infinitesimals (presented informally) rather than limits is definitely a big deal, and I think you will have to read the book for yourself to see if it works for you. When ...
- 149
3
votes
Entertaining and fun books about mathematics for (basically) liberal arts students
Permit me a possibly unusual recommendation:
Alexander, Amir. Infinitesimal: How a dangerous mathematical theory shaped the modern world. Macmillan, 2014.
Most of the action takes place in Europe ...
- 29.5k
3
votes
Entertaining and fun books about mathematics for (basically) liberal arts students
Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension, by Michio Kaku. A little long to be light reading, but I love the chapters at the beginning discussing ...
- 553
3
votes
Imbuing a six year old with a sense of mathematical wonder
Base 2 counting on fingers - gets you up to 1023.
Base 12 counting - need two more numbers flip & flap. 1, 2, 3, 4, 5, 6, 7, 8, 9, flip, flap, flap-one, flap-2, flap-3, flap-4, flap-5, flap-6, ...
- 39
3
votes
Imbuing a six year old with a sense of mathematical wonder
Try folding a piece of paper in half, then in half again and see how many times you can do it. start with A4 then find larger pieces-newspaper then wallpaper perhaps.
- 31
3
votes
Mnemonics for some properties in mathematics
Here is my way of memorizing the three main trigonometric functions. An angle $\theta$ is in standard position locating a point $(x,y)$ on a circle with a radius $r$ centered at the origin. There is ...
- 10.8k
3
votes
Mnemonics for some properties in mathematics
First heard it from a former classmate of mine, might be her own invention:
When the second derivative is positive, the function is happy (i.e., its graph looks like a smile). When the second ...
- 500
3
votes
Is Calculus Made Easy by Silvanus P. Thompson a good book for first-time calculus learners?
In a sense it is OK. In the sense that almost any book (except for one that is very difficult, and assigned to a weaker student and/or one without strong motivation to prevail) is OK.
It's really ...
- 39
3
votes
Pi Day is approaching: What are some interesting math questions whose answer is exactly $\pi$?
A favorite is:
What fraction of the integer lattice can be seen from the origin?.
The answer is about $61$%.
Here $\pi$ makes its appearance in a surprising, non-circular context
(surprising to me):
$$...
- 29.5k
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