
BetterExplained: Math Lessons That Explain Concepts - rfreytag
http://betterexplained.com/
======
typon
This site is a hidden gem on the internet. This guy deserves a lot more
credit. I think he's doing something at the level of Khan Academy, but for
seemingly simple concepts we all take for-granted.

An article I really enjoyed was his explanation of Quake's inverse square root
method:
[https://web.archive.org/web/20150530232103/http://betterexpl...](https://web.archive.org/web/20150530232103/http://betterexplained.com/articles/understanding-
quakes-fast-inverse-square-root/)

What I also appreciate is that he admits when he doesn't understand something
and doesn't pretend to give an incomplete, vague explanation and just straight
up says he does't fully get it (like why the specific 'magic' number in the
Quake algorithm). Thankfully he linked the original paper and I read up on it
myself. But his initial explanation provided a solid background for the paper.

~~~
kalid
Hey, Kalid from BetterExplained here, thanks! My general philosophy is to be
really, really honest with myself if I understood something. It's ok (really!)
to admit when we haven't fully understood a concept.

Want a fun example? How about percentages. Yeah, that thing we mastered in 4th
grade or whatever. That thing we use every day.

Well, did you know that

a% of b = b% of a?

Let's say you want 16% of 25. Ugh. Ok, let's multiply it out... divide by
100... no!

How about 25% of 16? Well, that's 4. Easy. But are they the same thing?

a% of b = a/100 * b

b% of a = b/100 * a

Either way, it's ab/100\. Now every percentage problem has a 50% chance of
being expressed more easily. How did we miss this? (Argh!!!)

Math is full of insights like that. Trig functions (sine, cosine, tan, etc.)
are actually themselves percentages. A sine of .95 means you are at 95% of
your maximum height (where the max is the hypotenuse). Sine and cosine are
unitless numbers, and that's why the can be each other's derivatives (the
percentage change of a percentage change...). So many things click! What else
have we overlooked?

Anyway, really appreciate the note!

~~~
themartorana
What?!

I've wasted so much of my life.

~~~
nickpsecurity
Me too. I was even a math geek but didn't understand most of it. I knew all
the rules for equations plus heuristics for how to apply most of them. I can
only imagine how much more effective I'd have been if there was a constant,
parallel learning process focusing on intuitive understanding of all
foundational concepts in various math branches.

------
TuringTest
I just love this guy's ADEPT method of exposition (Analogy, Diagram, Example,
Plain English explanation, and just then Technical definition). [1]

That is exactly how I like to be introduced to any new concept, in special
when I'm a complete newcomer to the field and can't relate it to previous
ideas in it. Judging by the reactions to the BetterExplained site, other
people agree with that.

[1] [http://betterexplained.com/articles/adept-
method/](http://betterexplained.com/articles/adept-method/)

~~~
igravious
I've found that I also need to understand the historical context/impetus... I
need to be shown and eventually understand why something was developed when it
was developed. I need chronology of thought and ideas.

For instance, learning about Gödel's theorems without having the Hilbert back-
story explained. Learning about Leibniz's and Newton's calculus without
learning about infinitesimals. And so on.

There's generally a reason _why_ concepts are born _when_ they are born. If
you think about your maths classes, sometimes you're instructed to learn a
method because it is useful and because it has real-world applications but it
I don't think anybody is ever first taught algebraic geometry properly, if I
may use that word. I don't think kids are taught the geometry is one thing and
algebra is another and that different spaces can have different metrics. Am I
making sense here? Do people see what I'm trying to get at?

Am I arguing for HADEPT? :) (Historical context, Analogy, Diagram, Example,
Plain English explanation, and just then Technical definition)

~~~
kalid
Great point. I find myself looking at the history of the idea when writing up
a post. Did you realize negative numbers were only accepted in the late 1700s?
That the Fourier Transform was originally rejected as untrue when first
presented, by world-famous mathematicians even?

(Yet we require students to internalize it without issue in a single lecture.)

Historical context is huge. I think I'm now stuck with this ADEPT name but
maybe it fits into the Plain English portion :).

~~~
igravious
> Did you realize negative numbers were only accepted in the late 1700s?

I did not know that! This makes total sense. I'd like to know more about that.
When you think about it, only whole positive numbers make sense from a
quantitative perspective. One thing, two things, three things, and so on.
What's half-a-thing? Right? a half-a-thing is still just one thing, if you
know what I mean. And how can no thing (nothing) be a number? And how can
negative numbers be "numbers". It has always struck me that imaginary numbers
are really badly named. Zero and the negative numbers are just as 'imaginary',
equally unintuitive from a certain perspective.

I applaud what you're doing. I think there is a metric-tonne of dogma and bad
naming schemes in the standard maths curriculum. Remember in software
engineering they say that naming things is one of the hardest parts of the
task? I think the same applies to maths, perhaps more so.

~~~
kalid
Exactly! There's a quote from a famous mathematician at the time that the
negatives "Darken the very whole doctrines of the equations". If positive is
good, negative must be evil right? And how can "less than nothing" exist? I
love the philosophical implications of it.

Ugh, tell me about the naming. "Imaginary numbers?" How about "rotated
numbers". Nobody complains "Hey, when will I ever use the second dimension?".
But "imaginary numbers" are setup to be eye-rolled.

------
rfreytag
Internet Archive has a copy:
[https://web.archive.org/web/20151221053341/http://betterexpl...](https://web.archive.org/web/20151221053341/http://betterexplained.com/)

>>>>> Please donate to the Archive while you are at it! :-)

Google cache:
[http://webcache.googleusercontent.com/search?q=cache:http://...](http://webcache.googleusercontent.com/search?q=cache:http://www.betterexplained.com/)

------
hugs
I needed a refresher on trig last year for some robotics simulations I was
working on. The trig lesson was extremely helpful:
[http://betterexplained.com/articles/intuitive-
trigonometry/](http://betterexplained.com/articles/intuitive-trigonometry/)

And fwiw, I finally learned an intuitive understanding of radians by reading
the Tau Manifesto (not on BetterExplained). It would be awesome if
BetterExplained used tau instead of pi in the lesson on radians, but that's a
minor nitpick for a very helpful set of lessons.

~~~
jeffwass
Out of curiosity do you get confused when people talk about 360 degrees, or 90
degree angles, or turning around 180 degrees, etc? Most people I know
intuitively understand degrees and could easily understand radians the same.

Why should BetterExplained use tau? Tau is a fairly niche idea that will only
confuse way more than explain. That's a bit like saying BetterExplained should
be written in Esperanto.

Personally while I agree that historically pi would have been better off if
defined as 6.28... instead of 3.14... (And even told my students this long
before tau manifesto came out) I don't feel that a factor of 2 warrants using
up a whole other Greek letter.

(I'd be much more supportive of "tau" if instead of the Greek letter Tau Hartl
chose a unique new symbol, much like physics uses hbar instead of h as he
Planck Constant for radians instead of cycles).

~~~
jerf
The anecdata that tau is helpful to learners is, IMHO, pretty strong at this
point. Facts beat theory. And since anecdata is all we have, well, it's all we
can use to talk about.

I think it's way, _way_ too easy for people on the terminal end of education
to forget just how easy it is to get tripped up by very, very little things.
Especially if they were themselves "good at math" and really aren't bothered
by extra factors of 2 flying around. This is not the normal experience.

~~~
jeffwass
When someone says 90 degree angle, does that confuse you?

~~~
jerf
As it happens, I've tutored people in the middle of high school geometry.
Radians confuse them. Full stop. If there is something that can make it easier
to understand, while at the same time sacrificing absolutely nothing of
mathematical consequence, it's a good thing.

What confuses _me_ is not the relevant issue. I've got $BOATLOADS of higher
ed. I'm not the interesting case.

~~~
jeffwass
Ok, we're far away from my original point which was only on using tau in one
website.

My actual only personal argument against Tao as Hartl proposed it is the use
of a standard Greek letter. Really would have preferred he picked something
that was more "backwards compatible", exactly as physicists did with hbar.

If you're for reducing confusion, do you think adding a new fundamental
constant to the body of mathematics that is a Greek letter already used for
countless other variables in history, will this cause confusion between old
and new mathematical science texts and papers?

Asking students of science for any texts and papers they read whether tau is
2pi or some other variable, and keeping track across them, seems more
confusing to me than just consistently using pi and extra factors of 2.

~~~
hugs
You have a valid complaint about reusing a letter that already had meaning in
other contexts. He does address that in the manifesto, though.

------
neilsharma
I've been using BetterExplained to review concepts I thought I mastered (based
on great test scores and grades) but years later realized I had zero intuition
on. It has been, by far, the most useful single source of math content I've
found on the internet. The world needs more people like you.

Two Questions:

1) What are your thoughts on interactive content like ExplainedVisually? I've
been thinking about doing something similar for data structures / algorithm
topics. How much of learning math concepts is exploratory vs learn-by-doing?

2) Are you running BetterExplained as a side business, or full-time? And if
you're willing to share techniques and numbers for the entrepreneurial HN
community, what are some things you've done to market it, monetize, etc and
what were the results?

Thanks!

~~~
kalid
Really glad to hear the site helps with new insights (especially for someone
who has aced the tests/grades). I was in a similar boat, qualified on paper,
but not in my heart of hearts.

1) In general I like any efforts to explain things in new ways, and
ExplainedVisually is great. My philosophy is that teaching is like humor. You
want to make something funny, present it well, but _not_ overexplain it. Let's
people enjoy the joke. If you do too much handholding, you ruin the surprise
and it's not fun to be told "Ok, the punchline is coming up...". It's not an
exact science, but you get a nose for when something is truly illuminating vs.
trying to chew your food for you.

2) BetterExplained is a side business. Happy to share numbers, etc. I have
some earlier posts about ebook sales and techniques:

[https://news.ycombinator.com/item?id=870015](https://news.ycombinator.com/item?id=870015)

I don't think I should be taken as a model of learning though (I write very
infrequently) but thankfully math is evergreen. Many of my most popular
articles are 5-7 years old.

I do want to dedicate more time to it. I realize I was afraid of ruining my
love of learning by turning it into a profession, but I'm slowly coming to
grips with it. That's one of the hardest parts for me actually, feeling I'll
kill the golden goose by squeezing too hard.

I'll probably do a blog post / postmortem on marketing, numbers, etc. so keep
an eye out :).

~~~
neilsharma
1) "Not over explain it" \-- that's really good advice. You don't want to take
the "aha" moment away from someone.

2) Thanks for the link! Definitely looking forward to your blog
post/postmortem (don't let BetterExplained die!). Have you found learning to
be less enjoyable by writing about it, or do you end up discovering a dozen
other tidbits of math magic you want to share with everyone?

Two more questions if you don't mind :)

3) What are your thoughts on word problems?

For example, in most linear algebra textbooks, you are given matrix and are
asked you to process it. Rarely are you given a word problem and are asked to
think through the entire process (data and operations matrices setup -->
processing --> meaningful end result).

4) For inspiration, what are you experiences explaining concepts in a cross-
disciplinary manner?

When I was a student, I never understood _why_ a concept is important.
Homework problems were abstracted out of all real-world context to train for
mechanical problem solving. Only now, after exploring data and writing
algorithms in health, journalism and finance, have I finally been able to
answer the question I always had as a kid: "why is this stuff useful?"

~~~
kalid
(Looking back at comments, replying to this a bit later.)

1) Exactly. It's like spoiling a movie.

2) Hah, the postmortem is more about the Reddit interaction (write up about
went well / things I'd change). I'm planning on working on the site as long as
I can. It's a life mission at this point.

Learning has stayed enjoyable, I tend to write insights that really strike me
and get excited to share. (Which leads to me studying it more and figuring out
new insights.)

When learning is drudgery (this happens often), I tend to let the topic sit a
bit, and I don't write publicly about it. The articles on the blog are what
genuinely get me excited about the topic. I do think there's usually a way to
see a topic that makes it come alive.

As an example, I'm working on quaternions. I have a large list of notes here:
[http://aha.betterexplained.com/t/quaternion/267](http://aha.betterexplained.com/t/quaternion/267)
and I'm slowly getting an intuition that I'll then work into an article.

3) I like word problems because they force us to ask the uncomfortable
question of whether we can think with the material (vs. follow the steps).
That said, this check of whether you're thinking or following steps can be
accomplished with other types of questions too. For me the method isn't as
important as the outcome.

4) Good question. So far, my audience is typically people who are self-
motivated (i.e., they have a test, are curious, need homework help, etc.) vs.
giving a talk to a potentially uninterested audience. (Not intentionally
uninterested, but a volunteer audience.)

The primary motivations to learn are probably:

* practicality

* curiosity

* beauty / awe

* sense of accomplishment

Depending on your audience you'd have to tailor it. But I think beauty/awe is
more powerful than we think. Even for a technical talk, I'd get people see the
aha! moment. It's the sugar that helps the medicine go down.

------
chairleader
Interesting set of articles. "Intuition isn't Optional"[1] could explain why
pursuing simple solutions and good naming is important in software.

[http://betterexplained.com/articles/intuition-isnt-
optional/](http://betterexplained.com/articles/intuition-isnt-optional/)

~~~
kalid
Nice point. Yes, naming can prime people to understand or be confused by a
topic. Renaming the "imaginary numbers" to the "rotated numbers" would make
them orders of magnitude easier to learn. "What's so strange about the second
dimension?" vs. "How do I understand the square root of -1?".

------
waprin
This site is absolutely excellent. There are a lot of things in math that I
sort of had a handle of the mechanics of, but less so the intuitions for,
which this site fills in well:

I really liked the explanation of sine as something that makes things
'circly'.

[http://betterexplained.com/articles/intuitive-
understanding-...](http://betterexplained.com/articles/intuitive-
understanding-of-sine-waves/)

Does the site take external contributions?

~~~
kalid
By popular demand:
[http://patreon.com/betterexplained](http://patreon.com/betterexplained)

:)

~~~
waprin
Sorry, I was asking if you accept article contributions.

~~~
anjanb
as a reader, I think that that should be nice. Also, it would be nice to have
a forum where ideas get exchanged. Then Kaled can decide if any of the
discussions should make it into the site as an article ?

~~~
kalid
Thanks for the feedback! I have a community in progress at
[http://aha.betterexplained.com](http://aha.betterexplained.com) \-- I have
some collaboration ideas I'll be announcing early next year :).

------
nickpsecurity
The article on math intuition plus the e article were incredible. I always
knew how to work with them and sort of what they meant but never really
intuitively. The articles were first time in a while that happened. Reminds me
when I first learned the often-hated word problems were the best part of math
that explained how to actually map it to real world. Equations took less
thought for me so I avoided lots of word problem practice. Was glad I shifted
back a bit before calculus or I'd never be able to explain what it was good
for.

This guy's site should get more attention and probably an award. I'll be
experimenting with less-math-inclined people to see how effective it is.

~~~
abc_lisper
Yeah, the e article is awesome. Cleared up a lot of cobwebs in my brain..

------
romaniv
After reading several articles I came to the conclusion that every Wikipedia
article on math concepts which are covered on betterexplained should _start_
with the link to betterexplained. I know it's not going to happen, but it
would benefit hundreds of thousands of people.

~~~
plaguuuuuu
I feel like it's often easier to learn concepts from equations. The
betterexplained articles are so wordy and contain so many analogies (some of
which are leaky abstractions) that there's all this noise around the core
concepts. Equations cut away all of that noise. And it's not like I'm some
huge maths nerd; I've always found language and philosophy far easier to learn
than mathematics.

Oddly enough, I find betterexplained much more useful when I have already
grasped the core concepts, because it does a great job of connecting to other
concepts.

~~~
kalid
Thanks for the feedback! I see the articles as a supplement to the formal
description people usually have in hand when they are googling for help :).
For the succinct formal definition I definitely recommend Wikipedia or
Mathworld.

------
kudu
Is there anything similar to this for physics? I'm taking an introductory
mechanics class and I can't help but think there must be a much more
intuitive, logical way to solve even complicated multi-step problems than just
falling into algorithmic pattern-based resolution.

~~~
kalid
I haven't done much physics, but Feynman is my teaching inspiration. He has
his famous lectures on Physics:

[http://www.feynmanlectures.caltech.edu](http://www.feynmanlectures.caltech.edu)

(Put online by Michael Hartl, of TauDay fame among others.)

I haven't gone through them extensively but Feynman was a master of making the
complex simple.

------
robbiemitchell
Tangent: with author permission, these lessons are loaded into the
recommendation system for Knewton's free learning service:
[https://www.knewton.com/](https://www.knewton.com/)

~~~
kalid
Awesome! (Kalid from BetterExplained here.) This goes for everyone, all the
articles are under a CC license.

------
elliotec
I bought the book a while back, and I still struggled with it. I have very low
math skills. My pre algebra teacher was a joke, and everything building on
that flew right over my head. I basically talked my counselor into letting me
graduate even though I didn't pass basic math graduation requirements in
college. So I'm a pretty clean slate, and this was quite difficult for me. I'm
a pretty good developer, but telling the computer to do math for you based on
looking up what it needs to do is much different from understanding the
concepts myself which has been a real difficult thing for me. Kahn academy is
the worst, like bringing back old terrible memories of repeating hellish math
problems that I don't really get, but still want to move on out of boredom.
Such it is.

~~~
kalid
Thanks for the feedback! The book is more of a "top concepts I wish I knew"
but not really a ground-up tutorial.

For starting from a clean slate, you might like:

[http://betterexplained.com/static/articles/rethinking-
arithm...](http://betterexplained.com/static/articles/rethinking-arithmetic-a-
visual-guide/)

Once you can visualize the basic operations (add, subtract, multiply, divide),
every new math operation becomes a lot easier (complex numbers = rotations,
exponents = growth, combining them = orbiting a circle...).

~~~
lstamour
When you say the opposite can be the multiplication of -2, did you actually
mean the multiplication of -1? It's a bit unclear in the example whether the
"loss of two" means 1 * -1 = -1 and therefore a relative loss of two, or 1 *
-2 = -2 or a relative loss of 3. I always figured opposite meant inverting
either the fraction so 2/1 becomes 1/2 or it meant multiplying by -1,
effectively toggling the negative sign.

~~~
kalid
Whoops, might not have been clear enough. In more mathy terms:

Multiplication by 2 means "1 (starting point) times 2 (scaling)"

If we "do the opposite" we can take the inverse of the starting point or the
scaling:

-1 (additive inverse of starting point) times 2 = -2

or reverse the operation

1 (same starting point) * 1/2 (scaling inverse) = 1/2

Of course, we assume the scaling term is what's being inverted, but it's
important to think about the meaning. There's a hidden parameter for these
operations and sometimes making it explicit can be helpful. (I.e., euler's
formula, e^ix, is better seen as 1.0 * e^ix. That is, you are starting at 1.0
then doing a rotation.)

------
wiremine
I wonder why more secondary teachers don't use these sorts of examples? Any
teachers out there that can give insight?

~~~
coldtea
Even if they did, students don't care for most things, intelligently explained
or not. That's a first problem to overcome.

~~~
ethanbond
According to...?

A lot of people love learning new things. It's the mode of learning them that
is offputting to so many.

~~~
akavi
Have you spent any time teaching unmotivated students?

Yes, ideally, every student would be motivated to learn for its own sake, but
for an individual say, 8th grade, teacher to get a class of kids to that point
is an enormous task. And yes, perhaps the entire education system should be
revamped so that kids never lose motivation, but _how_ to do that is hardly a
solved problem.

Which means "Here's the deeper principles that motivate this problem" is going
to have a huge uphill battle against "just tell us how to do the problems that
are going to be on the test", or worse, "this has no relevancy to my life, so
I'm going to tune out this entire class".

~~~
typon
I have taught kids ranging from 6 years old to 2nd year University undergrads.
The really young kids were in the setting of a coding bootcamp while the 2nd
year undergrads were in a Tutorial. I'm just prefacing my comment by saying
that I've experienced a large range of ages and abilities.

I always see this excuse as a failure of the teacher, rather than the
students. I believe students _want_ to learn, and the non-motivation is
usually a result of something that isn't so hard that the teacher can't get
around it. I used to feel that way before and only gear my lessons towards the
motivated ones (why should I waste my time on kids who dont want to learn?),
but I realized that it was I who was not motivated enough to get through to
those kids. The movie "Stand and Deliver" portrays what I'm trying to say in a
really fun and useful way.

I think teachers need to be held to a higher standard and blaming their lack
of success on students should be the last resort, after everything has been
tried. Sure you'll get some really pathological cases where the student is
absolutely unreachable, but I think that's so rare that it's not worth talking
about.

~~~
coldtea
That seems like an a-priory assumption.

I think it depends on overall context (socio-economic status of parents, what
they see everyday, what other teachers do, what the policy of the school is in
general, what their society at large perceives as success, etc.).

Empirical observation however -- and I've taught 2 different secondary schools
myself although just for a couple of years -- tells us that some students are
motivated and others are not. The teacher can try and nudge them towards the
subject, but it wont do that much with most of the unmotivated students. My
experience has been in what in the US you'd call "inner city" schools btw.

I'm not saying that this is an absolute rule, so individual counter-examples
don't really negate this, unless they do indicate a reverse GENERAL trend.
Sure, you could get a greatly motivated student even in a crappy school with
crappy teachers, the question is how often would that happen.

I also don't agree that the teacher should be "held to a higher standard" (at
least when meant to an extreme). Sure, there are indeed crappy teachers.

But students should come into school willing to learn and respecting the
environment, something that's not always the case. It shouldn't be up to the
teacher to do some special stunts to get the students basic attention --
instead of, say, playing mobile games on their smartphones, talking to each
other loudly, even listening to music on headphones.

~~~
typon
I think its the teachers job to earn the students' respect, by not only being
a role model but also demonstrating genuine interest in the topic they are
teaching. I think that when I show how deeply I love the topic I'm teaching,
it rubs off on the students and they go along with it.

Also, you seem to be arguing from the perspective of what _is_ rather than
what _ought to be_. I'm arguing for a shift in perspective where teacher
competence and enthusiasm and high expectations of students isn't something
special or extra, but rather the norm.

~~~
coldtea
> _I think its the teachers job to earn the students ' respect_

Students should have a respect for school (and the role of the teacher) before
any other kind of respect can be earned by the teacher as an individual.

Or, to put it another way, earning the students respect as a teacher is OK.

But having to earn the attention, and having to fight against students making
noise, playing, ignoring the lesson etc, should not be the case.

> _I think that when I show how deeply I love the topic I 'm teaching, it rubs
> off on the students and they go along with it._

As I said, assuming the teacher is capable and passionate, it still depends on
the students. Depending on the school/area/class/etc some students wouldn't
care even if Alan Kay taught them programming and Richard Feynman did physics.

The idea that students will be captivated by a passionate and eloquent teacher
doesn't always pan out in reality. A lot of times it's more like:
[https://www.youtube.com/watch?v=Bdf_XdDwc-o](https://www.youtube.com/watch?v=Bdf_XdDwc-o)

> _Also, you seem to be arguing from the perspective of what is rather than
> what ought to be._

Well, to get things to where it "ought to be" you should first tackle and work
with "what is".

------
chris_wot
I love this site. This explained logarithms and exponential growth _really_
well.

~~~
kalid
Glad to hear it helped, thanks.

~~~
chris_wot
Oh! Dude, you are _amazing_! Seriously, I don't normally say that to people -
I can't thank you enough because you honestly got me over a few mathematics
hurdles.

If you ever have a paid subscription, I'm buying :-)

~~~
kalid
Thanks Chris, really appreciate it. Hearing when the site clicks with someone
is invigorating.

No real paid subscriptions yet but it's a great idea =).

------
southclaw
I'm so glad this exists going into my next term involving a lot of maths that
I just don't fundamentally understand; sure I can remember a set of rules
after boring revision of sequences of instructions but I hate that.

I asked what a "dot product" _meant_ once and was just told how it could be
used to determine these other values. I later learnt what it actually was by
reading some renderer library code.

I had a similar "aha" moment when I read how you described sine/cosine/etc as
percentage values in relation to positions around the circle. I hate how I was
taught maths since secondary school (when I was so confused at trig/pythag
lessons but learnt the concepts very quickly when I was coding around with
positions and angles in a game engine mod to get a position x units in front
of a character instead of doing homework)

I really think this site will help me in the coming year, thank you!

------
darkerside
From: [http://betterexplained.com/static/articles/rethinking-
arithm...](http://betterexplained.com/static/articles/rethinking-arithmetic-a-
visual-guide/)

1 * x^2 = 9

"What transformation (“times x”), when applied twice, will turn 1 into 9?"

That's such a great way of thinking about algebra. The "understood" 1 is
equivalent to, e.g., an understood "YOU" in the English language.

~~~
kalid
Beautiful way to put it! We aren't always explicit about the subject of the
transformation. Similarly, when working with exponents, I think:

e^ix

is really

1 * e^ix

That is, we're starting with 1.0 and doing a transformation (rotation) on it.

------
outlace
This is great, wish someone would do this for more advanced math like
topology, or other more abstract/pure math

------
alblue
Seems like the site has gone down with traffic and CloudFlare is serving up a
generic 522 error page.

~~~
pixelkicker
Yep, bummer I was looking forward to checking this out.

~~~
hugs
Check back later when traffic has died down. The site really is worth a read.

~~~
kalid
Thanks! Working on getting a fully static version of the site up. Argh,
Wordpress with even caching plugins, still folds. (It's on reddit and getting
100x normal traffic). Eventually a postmortem will be in order.

Static links to some favorites:

• Imaginary numbers:
[http://webcache.googleusercontent.com/search?q=cache:http://...](http://webcache.googleusercontent.com/search?q=cache:http://betterexplained.com/articles/a-visual-
intuitive-guide-to-imaginary-numbers/)

• Understanding e:
[http://webcache.googleusercontent.com/search?q=cache:http://...](http://webcache.googleusercontent.com/search?q=cache:http://betterexplained.com/articles/an-
intuitive-guide-to-exponential-functions-e/)

• Intuitive Trig:
[http://webcache.googleusercontent.com/search?q=cache:http://...](http://webcache.googleusercontent.com/search?q=cache:http://betterexplained.com/articles/intuitive-
trigonometry/)

• Calculus intro:
[http://webcache.googleusercontent.com/search?q=cache:http://...](http://webcache.googleusercontent.com/search?q=cache:http://betterexplained.com/calculus/lesson-1)

• Sine waves:
[http://webcache.googleusercontent.com/search?q=cache:http://...](http://webcache.googleusercontent.com/search?q=cache:http://betterexplained.com/articles/intuitive-
understanding-of-sine-waves/)

• Euler's Formula:
[http://webcache.googleusercontent.com/search?q=cache:http://...](http://webcache.googleusercontent.com/search?q=cache:http://betterexplained.com/articles/intuitive-
understanding-of-eulers-formula/)

• Linear Algebra:
[http://webcache.googleusercontent.com/search?q=cache:http://...](http://webcache.googleusercontent.com/search?q=cache:http://betterexplained.com/articles/linear-
algebra-guide/)

~~~
kalid
Update, I've made a static version of the site
([http://betterexplained.com/static/](http://betterexplained.com/static/))
which you can browse. I'm redirecting requests there.

------
akerro
>Secondly, if he is not involved in criminal activity, why does Mr Claus use
unbreakable encryption?

How do they know he encrypts everything?

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jgamman
shoutout to kalid - love your work.

~~~
kalid
Thank you!

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tempodox
Error 522

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andrewclunn
Aw, and here I was hoping for clips from SquareOne TV...

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houzi
Is it a data mining site? I'm just entering captcha's for days..

