Tuesday, January 22, 2019


--- Spanish ---

I have a couple of useful tools outside my Spanish study materials.

Who needs a Spanish to English dictionary when you can type "translate spanish to english" into the Google search bar to come up with a Spanish to English translator. I hope it doesn't become  a crutch. I also hope that, if I see the words enough times, they will stick.

Google provides many instant helps in their Internet search utilities. For instance, you can type "convert inches to cm" and you have an Imperial length to metric length converter. "google help" or the following address will give you a lot of information about what you can do with Google.

https://support.google.com

Also, in Denver, most public notifications, including many labels on groceries, clothes, and such, are in Spanish. I already know many Spanish words from just shopping and riding on the RTD.

Tags: Spanish, Google tools

Thursday, January 17, 2019


--- The Capitol ---

Denver has a lot to offer the adventurer - a lot of culture, history, technology, art, food, sports, entertainment...but the first fact about Denver is the capitol. For everyone outside of Denver, Denver is the Capitol of Colorado.

Buses stop all around the Capitol building, so it's not hard for the pedestrian to get there. Coyote and I took the D Line to the 16th street mall and walked south - it's not a long walk and it's easy to enjoy the street life at any time of the day. Not long ago, I attended a town meeting at Civic Center Park and ended up walking up 16th Street Mall after dark. I think, if I wanted to recommend a city to a friend for night life, it would be Denver.

Civic Center Station, the big downtown bus terminal, is at the south end of 16th Street Mall and the capitol is just across Colfax from that - you can't miss it.


                                                                      [The Capitol]

The visually most outstanding characteristics of the building are the sheer size and the gold dome. The original dome was copper, but Denverites rejected the use of copper and pushed for the more natural gold. Only 4 pounds of the stuff is needed to cover the entire 2842 foot square surface. Although the gold is from Colorado, it is sent to Italy to hammer into the thin foil, thinner than a human hair, used to cover the Capitol dome.

Ten other states have gold domes on their Capitols and two others have gold cupolas. Gold is popular. Many of the states just buy their gold. The Denver dome is gilded with gold from Colorado mines.

In fact, most of the materials used to construct the Capitol building are from Colorado. The Yule Marble used in the floors and stairs, from Marble, Colorado, is also the marble of the Lincoln Memorial and Tomb of the Unknown Soldier in Washington, D.C. The rose onyx used for the walls is from near Beulah, Colorado, is unique in the world, and is almost all in the Capitol - so don't go to Beulah to see rose onyx - it's all here.

                                                                [Rose onyx walls]

                                                                         [Grand stair case]

Only the brass (there a four or five people employed in the Capitol just to polish the brass fixtures) and white oak are from other states. The brass is from Cincinnati, Ohio and Louisville, Kentucky, and the oak is from the Ozarks in Arkansas and Missouri.

I couldn't take enough pictures nor could I fit them into a blog. The building is packed with art objects

                                               [Murals on the first floor rotunda walls]

The tour took us up the rotunda (stairs, lots of stairs) to some of the room galleries and balconies and behind the scenes to see the inside workings. The copper dome is still there. Most high peaked domes like the one on the Colorado and U.S. Capitols are more ornamental than stable and overlay an inner spherical dome.

                                                              [The rotunda]

The United States says "government for the people, by the people, and of the people," Colorado enacts it. There is every opportunity for the citizen to be active in Colorado government. When Colorado says, "This is your Capitol," they back it up.

Even the security staff at the Capitol building were friendly, helpful, and professional. The tour guide reminded us several times that, when the tour was finished, we were free to look around all over the building.

The Capitol building houses the headquarters of two of the three branches of Colorado government - the executive and legislative branches. The offices of the Governor, Lieutenant Governor, and Treasurer are on the first floor, and the House of Representative and Senate chambers are on the second floor. There are galleries on the third floor where visitors are welcome to observe legislative proceedings. Videos of proceedings are archived and are available on the Internet at https://www.coloradochannel.net .

The Colorado Supreme Court is housed across the street in the Ralph L. Carr Colorado Judicial Center Building across the street. I haven't made it there yet, but it's on my list.

The House chambers is painted blue and the Senate chambers is red like the Parliamentary chambers in Britain.

                                                                  [Senate chambers]

                                                               [House chambers]

Although much of the Capitol is as it was completed in 1901, as you can see, there have been  modernizations like the electronic call board on the wall of the House.

Stairs - many, many stairs. The Capitol tour takes you all the way up to the outside balcony of the dome, where the views are spectacular. At the west end of Civic Center Park (see the mountains?) is the City and County Government Building.

                                                               [The view west]

Just across the street to the southwest is the Ralph L. Carr building of which I spoke above. It has roof greenery.

                                                             [Ralph L. Carr Building]

Down the street is the Cathedral Basilica of the Immaculate Conception with it's towering Gothic architecture.

                                         [Cathedral Basilica of the Immaculate Conception]

After the tour, I shot some street views.

                                                                         [Colfax]

The sun was in a bad place so many of the pictures were blurred or glarey. I did manage to get the statue around back of the Native American examining a buffalo carcass. It is called "The Closing Era" and it was created by Preston Powers for the 1893 Colombian Exposition in Chicago. The name is, perhaps, a little short sited as Native Americans are reclaiming much of their "lost" cultures and heritage. Maybe the "era" was just closed for some housekeeping.

                                                              [The Closing Era]
Well, hopefully, if you are a Coloradan, you will take this tour. I've included blogs about Civic Center Park in the past and I'm sure there'll be more to come. The government buildings are scattered for several blocks around Denver and there are many statues and other works of art and history - I can't even begin to cover them all.

I've visited the seats of government in Washington, D.C.; Atlanta, Georgia; and Montgomery, Alabama and have seen many of the other Capitols from some distance. They're all spectacular. Most of them provide tours and you should also check to see how you can sit in on legislative hearings.

What they do in these government buildings affects your life deeply.


Sunday, January 13, 2019


--- Terminus: Union Station ---

Gold drew people to Colorado, but the promise of gold in the area that is now Denver proved to be illusory, so Denver restructured as a supply hub and thrived. Early settlements lay south of present Denver along the South Platte River and it's tributaries - Petersburg, Montana City, Auraria. Denver City grew across Cherry Creek from Auraria and when a bridge was built across Cherry Creek, the two settlements merged to become Denver.

The Union Station area was the location of early Denver.

On 1/8/19, I took the RTD E Line from University Station to it's terminus at Union Station, the central hub of the Regional Transportation District in Denver. At this point, 17th street is a mall with the light rail station at one end and the old Union Station building at the other.

                                                                 [17th Street mall]

                                                                 [Light rail station]

The mall includes the underground buss terminal and the Amtrak station, which will soon be the terminus for the light rail G Line out to Wheatridge.

The Amtrak station has light canopies that are sturdy because of their curvature. You can see the effect for yourself by holding a sheet of paper by one hand and trying hold something like a pencil or marble on it. The paper, of course, just collapses. Give it a slight valley and it will hold up a surprising amount of weight.

                                                              [Train station canopy]

The old station, built in 1881, burned in 1894, but was rebuilt in 1914. The whole complex was completed in 2012. The station house, reminiscent of many large city central stations with it's high arched windows, now houses the 112 room Crawford Hotel, several restaurants and shops, and a large train hall.



                                                                   [Union Station]

They were taking down the tall Christmas trees while I wandered around.

I once took the Flatirons Flier bus to Boulder. It leaves out from the Union Station mall. I wandered around the LoDo (Lower Downtown Denver) area for sometime before asking where the buses were.

They were underground. There are two pavilions at street level that house stairs and elevators to the underground bus terminal.

The ticket sellers are located in the underground bus terminal and I had some expired ticket books I needed to exchange. This time, I knew where I was going.

                                                                      [Bus terminal]

Merging back out into the sunlight at Chestnut Place, I was back at the light rail station and, looking west, saw the Millennium Bridge. I've seen a lot of reviews of the Millennium Bridge that remarked, "What's so special?"

Well, that's easy. It was the first of it's kind. It was one of three bridges begun in 1999 to connect the Highland community with LoDo. Before then, pedestrians would have to cross an interstate highway, a river, and a train yard to get to downtown Denver.

The Millennium Bridge crosses the train yard. It had to fit between some high bridges and the design was to provide a relatively small incline from street level, so an innovative cable-stayed design was used with a single 61 meter steel mast (the whole thing looks a lot like a pontoon boat with a single sail mast) to support the cables that support the walking deck. It is only 8 meters above street level, and it spans 40 meters (130 feet for you Imperial measurists) with a clearance of 61 meters (200 feet).

The Wikipedia has an informative article on the bridge here: https://en.wikipedia.org/wiki/Denver_Millennium_Bridge




                                                            [The Millennium Bridge]

It's also famous for having been in a movie (The Frame) and engineering documentaries - notably Stephen Ressler's Teaching Company presentation - Understanding the World's Greatest Structures.

I was a little unsure about how to proceed from the Millennium Bridge to see the other two bridges but I shouldn't have been. From the deck of the Millennium Bridge, the other two were in sight just to the north.

                                             [Commons Park from the Millennium Bridge]

Just north of Union Station is a strip of greenway along the South Platte River - Confluence and Commons Parks. If I had continued my hike north of Alameda on the Platte River Trail instead of moving east into Denver on my station-to-station hikes, I would have ended up here. Historically, this was a popular meeting place for Native Americans until gold was found here in 1858. Gold and water was the reason Denver was built here to start with.


                                                        [Speer Boulevard Bridge]

Looking west along Commons park (see the mountains?), I saw the Speer Boulevard  Bridge over the South Platte River. This is a classic steel arch cable suspension bridge. Cable risers hang the road bed from the arch. Just this side of Speer Boulevard is a more modern looking single span bridge that carries 15th Street and pedestrian traffic across the South Platte.



                                                               [Platte River Bridge]

The second of the  Highland access bridges is a light sidewalk held up by cables from two thin towers anchored midway the span. This bridge carries pedestrian traffic across the South Platte.

                                                                     [Platte River]

The 15th Street bridge separates Commons Park from Convergence Park, where Cherry Creek joins the South Platte. Here, the South Platte takes a turn to the east where it will join the Platte River far down stream in Nebraska near Ogallala. Cherry Creek, one of the larger tributaries in the Denver area, arises on the high plateau south of Denver and flows through Castlewood Canyon before becoming an urban stream.





                                                                     [Highland Bridge]

The Highland Bridge crosses Interstate 25. It is one of the three cable stay bridges and is the latest, having been completed December 16, 2006. The 325 foot long walkway is suspended under the sweeping arch constructed of steel pipe.

                                                            [Shoe hanging on the arch]

I thought this was a Southern thing. Down there you can see shoes hanging on power lines.


                                                                     [Confluence Park]

Cherry Creek isn't terribly spectacular, but the Platte River and most of it's main tributaries can become impressive when the weather is right - during the infrequent rain storms or when the snow pack melts from the mountains.

19th Street crosses the Platte River at the eastern end of Commons Park over an ornate steel trestle bridge.



                                                                [19th Street Bridge]

                                                                      [19th Street]

Following 19th Street back into town (I wanted to see Sakura Square and it is on 19th Street) is not as simple as it sounds. You have to get back across the train yard. Fortunately, there is a pedestrian bridge at the eastern end of Union Station that will do the trick.

                                                [Amtrak station from pedestrian bridge]


                                                                   [Sakura Square]

Sakura Square is a city block at 19th and Lamar Streets with a two story building with shops. The Japan American Society of Colorado has an office there on the second floor that (apparently) provides exhibits, but they were closed.

There is a small Japanese garden that commemorates three key figures in the Japanese American community.


                                                              [Yoshitaka Tamai]

Yoshitaka Tamai was a Buddhist priest who, born in 1900, moved to Denver in 1930 to establish the Buddhist temple at 20th and Lawrence Streets. The apartment complex at Sakura Square, Tamai Tower was dedicated to his memory in 1977, and the statue in the garden was placed on Sakura Square in 1996.

The engravings on the other statues, in white stone, didn't turn out well in the photographs, so you'll just have to visit Sakura Square to read them.

                                                                [Minoru Yasui]

Minoru Yasui (1916-1986) was a Japanese American lawyer and activist who was born in Hood River, Oregon. After internment in an American concentration camp during most of World War II, he moved to Denver in 1944. He received the Presidential Medal of Freedom posthumously in 2015.

The Wikipedia has a good article on the life of Minoru Yasui here:

https://en.wikipedia.org/wiki/Minoru_Yasui

                                                                    [Ralph Carr]

Colorado governor from 1939 to 1943, Ralph Lawrence Carr (1887-1950) supported the Japanese American cause during their internment in the concentration camps of World War II and afterward, the establishment of the Japanese American community in Colorado. He was the only elected official in the United States to publicly apologize for the treatment of American citizens of Japanese ancestry and that, arguably, cost him a U.S. Senate position.

I plan to visit the Ralph L. Carr Colorado Judicial Center in a few days and I will report on my trip afterward.

After eating at Sakura Square, I headed down Lamar Street to 15th Street and back to the light rail station at Union Station. From University Station, I walked to La Belle Rosette's for a signature espresso, and then to home. (jiggledy jig)

Bridges can be fascinating if you know how they work. There may be a famous one close to you. Take some time to really look at the bridges around you and see if you can figure out how they support their load.

If you want an in depth analysis of any of the interesting structures in Denver, Steven Ressler provides it in Understanding the World's Greatest Structures. Actually, I would recommend anything by him. He's knowledgeable, has a knack for getting difficult concepts across, is playful, and loves a good demonstration.


Tuesday, January 8, 2019


--- Remembering the numbers ---

My memory has never been that great. I've mentioned elsewhere that my grades were not that good in high school, but I made it through and found that, to survive college, I was going to need help. I found it in a book by Harry Lorayne and Jerry Lucas called "The Memory Book". It's still in print along with other books by Lorayne.

There might be those out there that remember Jerry Lucas as a basketball star - and he was, but if you look at his Wikipedia article, you'll see that he's also remembered as a memory educator. To publicize the Memory Book he memorized half the New York phone book. "Why not all of it?" you might ask> Have you ever seen the New York City phone book?

Anyway, I whole heartedly recommend the Memory Book for anyone that wants to improve their memory. It builds on the Major system for memorizing big numbers and association for remembering lists of words and goes on to explain how you can remember spatial information like map locations. I used it in organic and pharmaceutical chemistry to remember complex organic molecule structures. About the only thing it doesn't handle is prose language and it even helps with that.

I won't tell you about the whole system here (get the book!) but, since we're talking numbers, I'll give you the major system.

You can easily turn big numbers into words and, if you link those words together into a story, you'll never forget the numbers. Here's how.

There are ten consonants in the English language. "Okay, wait," you say, "there's way more than 10 consonants in the English language." but many are formed alike. For instance, j, ch, gee sound very similarly because they're all made by placing the tip of the tongue against the roof of the mouth and blowing air around it in a short burst. Here are the consonants and the digits they represents.

t,d - because there's 1 down stroke in "t" it represents 1.
n has 2 down strokes, so it represents 2.
m has 3 down strokes, so - 3.
r - four ends with an "r" so r reminds you of 4.
l - when you hold your hand out with your 5 fingers spread out, the thumb and first finger is in the shape of a capital "L" so "l" represents 5.
j is almost a backward 6 so j, ch, sh, and gee represent 6.
k and g (as in "get") - you can place two 7s together to form a k, so it's easy to remember that "k" represents 7.
A small cursive f looks like an 8 so f, ph, v all represent 8
P is practically a backward 9, so p or b represents 9
and z and s represent 0.

With all that, you can make words out of any number. Say you want to remember your computer's IP number and it is 76.5.27.159. 76 becomes k-ch. Since the vowels have no numerical value, you can use any of them to fill in the gaps, so 76 could be "catch".

5 becomes "l" so 5 can be "eel", Catch an eel doing what?

Well, 27 becomes n-k so you might catch an eel knocking on something.

It's all waterworld for eels, so 159 becomes t-l-p and it's obvious that you caught an eel knocking on your pet tilapia. Oh yeah, the stories you make up out of your number words should be ridiculous so you will remember them.

This system takes a while to explain, but it's really easy to remember and very quickly becomes second nature. I found myself driving around memorizing license plate numbers. One of my exercises was to memorize all the states of the United States, their capitals, populations, highest points, and elevations of highest points.

Even with the system, your memories have to be refreshed occasionally and I've long ago forgotten what I memorized but I retained it for years.

I use it now for remembering partial calculations in long mental mathematics problems.

Try it out. You'll be surprised at how easy it is.

Friday, January 4, 2019


--- Watching your language ---

A few notes on the choice of words........

Chameleons and the big word

I've never been punched because of something I've said. Amazingly, I've never been punched. A few times I should have been.

I'm a chameleon - you know, those lizards that change colors to blend in with their surroundings. I pick up accents, gestures, expressions.... I can't, say, affect a New Zealand accent if I try but sometimes one just comes out. I got that accent from a welder I worked with offshore.

I was driving around Montgomery, Alabama with a friend and we pulled into a fast food restaurant to pick up something to eat. The check-out person asked if I was from Australia and I said, "Yeah. I'm from Sydney." She oozed as I snagged my bag of food.

I don't typically lie by nature, but it was just too tempting, and it made her happy.

I was in a check-out lane at WalMart when I was suddenly rattling on in an Hispanic accent, and I turned around to see a big Hispanic guy and his pequena espousa glaring at me. I apologized profusely.

Sometimes, I can't pull out the word I want to use. I combat that problem by having a big vocabulary so, if I can't retrieve one word, I'll just use a synonym. Unfortunately, the synonym might be a $20 word where a half dollar word would be more appropriate. It makes me seem to be trying to impress people with my erudition.

It's tough being a lizard.

But, all in all, I've gotten along pretty well with my language problems. Here are a few things that I've picked up.

Big sentences

The Teaching Company has a course called "Building Great Sentences: Exploring The Writer's Craft" presented by Professor Brook Landon. One of his points was that Strunk and White was wrong in their "The Elements of Style" when they counseled to always use short sentences.

I agree.

Long complex sentences can be awful - a misery to try to decipher, but they can also be beautiful and fun to read if they are well crafted.

It's a matter of style. I hope my style in this blog is enjoyable to read.

The way I try to ensure that my long, complicated sentences are well crafted is: I read them aloud (or I listen to my computer read them to me - I put each blog through a screen reader before I post it.) If a sentence doesn't flow well, if it doesn't sound natural, if it's hard for me to get it out, then I start looking for a problem.

The age of belle letres is gone and I lament it's passing. I read letters of Civil War soldiers writing home or pioneers writing to their families back east and, although the writer is obviously illiterate, to the best of their ability, I can tell that they are trying to make their letter enjoyable, readable, beautiful. Even scientific works were crafted to be read - not like the dry scientific writing of today.

I want these blogs to inform, but I also want them to entertain. I hope you enjoy my stories of adventures in learning.

What is vulgar?

"Vulgar" is dirty, right? At the very least, it's uncouth.

Actually, it's Germanic.

The word "vulgar" actually means "common". For instance, the Bible was written in vulgar languages. The New Testament was written in a form of Greek called "koine" which literally meant "common". And, of course, the Vulgate Bible was called that because it was written in the vulgar Latin.

Today, vulgar usually means Germanic. I'll try not to be too offensive but I will talk about "ass". Of course an ass is a donkey and when you are calling a person an ass, you are likening them to a donkey.

But the use of "ass" (a word of Germanic origin) to refer to the "posterior" or "gluteus maximus" (both words from Romantic languages) is considered obscene, or, at least, boorish. Why? They mean the same things.

Well, there is an answer. It's the same answer as to why we raise pigs, but we eat pork. We raise cattle, kine, bulls, and cows, but we eat beef. Deer run in the forest, but when we eat them, they are venison.

On Christmas Day 1066, William the Conqueror was crowned king of England. "Conqueror" is a bit strong for what actually happened. William might have been French, but he was also related to the childless king of England, Edward the Confessor, so when the king died, William became a valid contender for the crown. Many in England, in fact, supported William.

When William became the king of England, one thing he brought with him was the French language, and it became fashionable to speak the king's tongue.

So, just think about the vulgarities that I'm not going to talk about in this article. How many of the inappropriate words are of Germanic origin while their appropriate alternatives are from the French, or Latin, or Spanish, or Greek?

Responsibility for being understood

I've mentioned James Kilpatrick as one of my favorite linguists. He held that the primary purpose of language was to be understood, and if your hearers understood you, then your language was correct. (I might also heartily recommend June Casagrande's book, "Grammar Snobs are Great Big Meanies: a guide to language for fun and spite".)

I would like to go a little further and suggest that people are responsible for being understood. Both the speaker/writer and the hearer/listener share 100% of the responsibility to be understood, for what other purpose is there for language except to be understood. Even double talkers carefully craft their language to be understood to be saying hilarious gobbledygook.

In speaking, the way you make sure that you are understood is by looking for nonverbal cues that you are making the right impressions on your hearers, and by flat out asking them if they understand you as saying what you meant to be saying.

When writing, well, you have to rely on the responses you get and those are not often forthcoming. But you use the same language speaking as you do writing, so you have some prior knowledge as to how others understand what you say. You should also be sensitive to the fact that persons from other cultures often use the same words differently, so, if your communications are to be consumed abroad, you should not be too surprised if you are sometimes misunderstood.

In that case, you should be the last person to be offended and the first person to be willing to correct misconceptions.

Choosing your words

Certainly, if you want to get a point across (or a concept, or an emotion, or a lesson) you should choose your words carefully and put them together in a may that will cause the consumer to be more likely to receive what you have to say rather than to wonder away, disinterested.

Humans have two advantages over all the other animals: excellent opposable thumbs and an exquisite technical language. It is entirely fitting that we should take the utmost care in crafting with both.

Develop a habit of listening to what you say and reading what you write. Don't be afraid to critique yourself and ask for others' feedback.


Tuesday, January 1, 2019


--- A course in mathematics ---

Do you want a self education in mathematics? I have three curricula for you according to how deep you want to go and how long you want to take.

If you just want a brief overview I'll plug my own work.

The Stat files (on the Therian Timeline site) are about statistics, but I begin by breezing through arithmetic, algebra, geometry, pre-calculus, calculus and differential equations - and then I throw in a little complex mathematics, vectors, linear algebra, logic, and simple statistics. The purpose of this section is to bring budding amateur researchers and statistician up to speed in the preliminaries, but the section, The Basics, would serve as an overview of mathematics, too. Here's the address:

http://www.theriantimeline.com/stat_files/the_basics

If you want a little more depth and, maybe, some hands-on experience, check out the Excursions section where I explain counting on your fingers (fingermath), standards of measurement (including the measuring tools you carry around with you everywhere - your body),  lattice multiplication, and building a slide rule from scratch using index cards.

http://www.theriantimeline.com/excursions

If you want a lot more depth, you might want to follow my mathematics LabBook. It's a mathematics tutorial with lots of personal involvement.  At the current writing, I've only covered the very basics of mathematics - the logic behind math, counting, and whole numbers, but my intention here is to look inside mathematics and really see how it works. Do you really know how numbers work?

If I live long enough, I'll make it to differential equations.

The LabBooks are LibreOffice Calc spreadsheet documents but, fortunately, LibreOffice is a free download.

http://www.theriantimeline.com/Mathematics.ods

..........................................
Level two is conversational math. You can pick up an understanding of mathematics to the point that you could sit through a lecture on, say, tensor analysis and understand what the presenter is talking about. You probably wouldn't be able to use tensors to solve an engineering problem though. You could achieve that level in about a year with the Teaching Company mathematics courses.

The Teaching company sells college level courses in a wide range of subjects. The video sets are pretty pricey. The key is that every set they sell goes on sale at least once during the year at a substantial discount. Also, the Denver Public Library has many of the products. Check your own local library if you want to go that way, but there is considerable advantage of owning your own. For one thing, there's no time limit.

The Teaching Company website is here:

https://www.thegreatcourses.com

For a complete course of mathematics, I would recommend:

Arithmetic
Secrets of Mental Math - Arthur Benjamin
Algebra
Algebra I - James A. Sellers
Algebra II - James A. Sellers
Geometry
Geometry: An Interactive Journey to Mastery - James S. Tanton
Precalculus (including trigonometry)
Mathematics Describing the Real World: Precalculus and Trigonometry - Bruce Edwards
Calculus
Change and Motion: Calculus Made Clear - Michael Starbird
Differential equations
Mastering Differential Equations: the visual method - Robert L. Devaney

There are several other sets for fields like discrete mathematics, probability, statistics, combinatorics, etc. but that might take you into a second year of study.
........................................................
Now, if you want to take a few years and really have a mastery of mathematics, I would recommend beginning with the CK12 textbooks and then switch to the MIT OpenCourseWare courses for the college level mathematics.

CK12 is an organization that offers excellent free textbooks and other learning materials for grades kindergarten to high school (thus "CK12"). The website is here:

https://www.ck12.org

And the MIT website is here:

https://ocw.mit.edu/index.htm

If you can get your hands on a copy of the old educational mathematics textbook Basic Mathematical Concepts, by F. Lynwood Wren it's one of the best mathematical texts for explaining elementary concepts I have seen. Some other great resources are:

The Universal Encyclopedia of Mathematics by James R. Newman
Secrets of Mental Math by Arthur Benjamin
The Handbook of Essential Mathematics: Formulas, Processes, and Tables Plus Applications in Personal Finance edited by Donald D. Gregory and Vincent R. Miller

This last reference is an Air Force Research Laboratory text that has been released for public distribution and can be found on the Internet here:
https://florida.theorangegrove.org/og/file/3a8c652c-11d0-e967-95fb-b5bbae2586d6/1/math_handbook.pdf

Also be sure to check out the Interactive Mathematics website (http://www.cut-the-knot.org).