Additional Math Pages & Resources

Friday, July 30, 2010

Numbers, Numbers, Numbers

I started thinking about Numbers - what can I say - I'm a math guy. I googled the word number, along with Poway, the town where Excel Math is located. Here's what I learned:

  1. The first meaning of Numbers is as a means of contacting people by telephone.
  2. Poway is going to allow Remote-Caller Bingo games, where the caller who supplies the bingo numbers comes from outside Poway. The city code starts like this: A. “Authorized organization” is an organization exempted from the payment of the bank and corporation tax by Sections 23701a, 23701b, 23701d, 23701e, 23701f, 23701g, 23701k, 23701l or 23701w of the Revenue and Taxation Code. “Authorized organization” also includes a senior citizens organization, a mobile home park association, or a charitable organization affiliated with a school...
  3. Gaines Manufacturing produces house number plaques and mail boxes. They're 3 blocks from us.
  4. Poway Unified School District standards include Number Sense (1st Grade) : Students understand and use numbers up to 100. They demonstrate the meaning of addition and subtraction ...
  5. If you want to start your own business, incorporate or form a Limited Liability Company in Poway, or if you are an employer, you need to obtain a Federal Income Tax Identification Number.
  6. On January 20th of this year, someone in Poway had a winning lottery ticket for $201,000! They got all but one lotto number (and so they missed out on winning $105 million).
  7. There are a number of interesting things for seniors to do, if they live at Brookview Village.
  8. If you want to know how much tax you pay to support the local school district, you need to have the Assessor’s Parcel Number (APN) for your property.
  9. In the past decade, a total number of 1783 government defense contracts were given to 142 companies in Poway, for a total value of $396,774,299.
  10. The Poway Unified School District is good compared to the norm in California ... the lowest school API score numbers are in the mid 700s and most are in the 800s. Here's a list of the top API scores in the Poway district:

    • Creek Side: 2006 API = 961
    • Deer Canyon: 2006 API = 947
    • Park Village: 2006 API = 940
    • Chaparral: 2006 API = 924
    • Painted Rock: 2006 API = 922
That's just about enough numbers for me today. It's a good thing we have plenty of experience from our elementary math educations to know how to use numbers ...

Thursday, July 29, 2010

The NEWEST and OLDEST things

This is an interesting question that involves math, values, perceptions and language. How do you decide what is old and what is new?

Is it the date and time of manufacture that determines age? 

If so, then electronic gizmos might be our newest items; after all, an iPhone4 has to have been made in the past 90 days...

 Is it when you buy something that determines its age?

In the automotive world, NOS (New Old Stock) parts are prized - they are "Brand New" but just discovered and being sold for the first time. Even if they are 50 years "old."

Is it when you yourself obtain something that the clock starts ticking?

"This car is new to me" or "I just got this 1950's prom dress"

There's no easy way to say what old and new mean. This is just one of the many ambiguities involved in mathematics! We have to address this in Excel Math, and in our everyday lives...

My wife and I have a small collection of icons. These are not little items you click on your computer desktop, but religious artifacts - paintings of Christian figures on wooden boards. They are meant to last for centuries, unlike the iPhone!

Here is the "oldest" one. It dates to about 1750, or before the Declaration of Independence. It was created in Russia. The previous owner was given it as a gift in 1917. I bought it earlier this year. It's old in most senses that we use the word "old".

Here is the "newest" one, a small icon of the Archangel Michael. An artist lady named Jacky created it in May 2010. I bought it from her on May 29th, so it's "new to this world" and "new to me" but it's not a new "image".

Here's the original image that it is modeled upon, which we think is about 700 years old. It's a very faithful copy, which is essential for Orthodox icons.

The very idea of the Archangel Michael is much older yet, since his first written appearance is in the Biblical book of Daniel which dates to at least 2200 years ago. I think I'll avoid the question of when he really came into being ...

Perhaps I am thinking about old and new because even though three of us at Excel Math are getting older (having birthdays soon),  Darcie who handles our telephone sales just brought in her brand-new baby girl. Here they are:

Wednesday, July 28, 2010

You talk too much!

Have you ever heard You talk too much! from family or friends?

Sunil Prabhakar did talk too much, in my opinion. I recently saw a claim for the longest (not distance, but time) telephone call. He talked non-stop for 51 hours.

Time to use some elementary math!

Q1. How many minutes are there in 51 hours?
A1. 51 x 60 = 3060

Q2. Who did he talk to?
A2. A whole bunch of other people. The phone at the other end was in a mall, and lots of people came to stand in line and talk with him.
Q3. How much did the call cost, using the standard rate on his mobile phone?
A3. I think he was given the call for free due to the publicity for the mobile phone carrier. They had technicians ready and making sure the call did not get dropped.

One reason for making the call was to prove that the phone carrier could dependably handle such a long connection.

Lots of people complain about long calls to customer service (mostly being on hold) and one record time I found was 6 hours to a customer talking about SHOES!!!

I've been trying to figure out how many words I have written per blog for the last year. Maybe tomorrow I will have a report for you. In the meantime, I have learned I've uploaded exactly 1000 graphics for use on the blog.

Here's a typical one.

Tuesday, July 27, 2010

Coins in the ashtray

Foolish me. I left my wallet in my desk drawer went I went to lunch, and had to use change from my car's ashtray to buy some food. Time to use my elementary math education, right?

Later I found a site today that promised to calculate the value of coins in a jar. Or in my case, the ashtray. I put all my remaining coins in a container, weighed the total amount, dumped out the coins, weighed the container, subtracted it from the total, and came up with:

1.10 pounds of coins in the ashtray

Then following the instructions, I grabbed a small handful of coins.
I counted out how many of each kind of coin:

7 pennies
5 nickels
5 dimes
3 quarters
20 total coins in the handful I grabbed.

According to the website, that equals a total of:

0.038581 pounds of pennies.
0.055115 pounds of nickels.
0.025000 pounds of dimes.
0.037500 pounds of quarters.

0.16 pounds calculated weight of handful
7.04 total handfuls in ashtray (estimated)
$1.57 value of my handful
$11.06 total estimated value of my coins

Actually I had $12.30 cents left, after the $2.18 I spent on food for lunch. So the calculator was inaccurate or my small handful was not a representative sample of the coins.

How does it work? They take the weight of the number of coins in the handful (assuming it's a normal distribution of coins to match the rest in the jar), they calculate the possible coins of each weight, then guess-timate a total.

Counting manually works just fine for me, because it took only about 2 minutes to sort the coins and count up my $12.30 - less than it took to do the coin counter web tool.

But if you have gazillions of coins, you need a coin counting machine. For some unexplained reason, we have 11 in our warehouse. Call if you want to buy one!

Monday, July 26, 2010

Come see our new web store

Wow. It seems like forever since I did a blog posting. In reality it was only a week while I went on a short vacation.

In the meantime we have also opened a web store for Excel Math, so people can order our curriculum online. It's been in development for about a year. We really started moving on it when ENSTORE (which links to our accounting system) started their beta testing.

I can tell you that it takes a lot of time and energy to create web pages, and even more to create a store where you can see the products, their interaction with other products (Student Lesson Sheet answers are in the Teacher Edition, Projectable includes a PDF version of the TE, etc.), calculate shipping, learn the sales taxes for your ZIP (postal) code, pay with various means, etc.

We have all this tied into our main accounting system so the inventory stays synchronized with orders from the web as well as the telephone, fax, mail, trade shows, etc. Part of the process involved going through and revising product codes, descriptions, pricing, etc for all our products.

Then I had to take pictures of every individual product so they could be accurately depicted in the web store. We'd never done that before. In some ways it's an easy task, but these three-box sets weigh about 80 lbs. When you have to move a bunch of the boxes, it's a chore.

Q1. How big a chore was it to photograph all the books?

Let's see:

We have 62 boxed set products, with an average box set weight of 25 lbs, so 62 x 25 = 1550 lbs.
We have 7 Student and 7 Teacher Editions at an average weight of 2.5 lbs, so 14 x 2.5 = 35 lbs.
We have 6 Projectable products at an average weight of 2.5 ounces, so that's about a pound.
Let's guess another 25 lbs for the Summer School products.
The grand total is 1550 + 35 + 1 + 25 = 1611 
I moved close to a ton of products that day in taking the photos!

It might seem like every company is able to take orders over the web, but that's not always the case. In our world, most customers are school districts and they buy using purchase orders and pay later with a check. That takes some special handling because state laws and regulations govern how these transactions occur. We haven't turned on the purchase order features.

One neat thing we discovered in our store is the ability to tell where our sales taxes are going. Look at this example:

You can see at the bottom right that California takes some tax, San Diego County gets some more, and Poway (poor city) gets nothing on the sale of textbooks. If you are outside California, don't worry, there's no sales tax.

It seems like this sample order is a pretty high total - almost $1100, but on the other hand, it includes a year's worth of math curriculum for lots of people.

Q2. How many people and how much per person?

A2. Let's see:
35 + 15 + 15 + 22 = 87 students + 2 teachers
$1092.67 ÷ 89 = $12.28 per person, including tax and shipping. 

What a deal - and everyone gets the same low price!

We wish we could offer more excitement in the sales process like our Southern California neighbor Cal Worthington but we're not that kind of business... and Brad doesn't like snakes.

Friday, July 16, 2010

Drawing to Scale, Part 2

This blog is all about using elementary math in our grown-up lives. Yesterday I left you hanging with a question:

Q1. If on a scale drawing 1 inch equals 32 inches, what scale distance equals 12 inches (1 foot)?

A1. Here's how we find the answer:

1.5 inches on the paper equals 48 inches in real life, so 1.0 inches equals 32 inches (48 ÷ 1.5 = 32)

We want to know what fraction of 1 inch equals 12 inches in real life. 
That is an unknown value which I will call X.

X is to 1 what 12 is to 32, or to say it another way, X÷1 = 12÷32

First we simplify the right side - the largest common denominator of 12 and 32 is 4. 
We find 4 goes into 12 three times and 4 goes into 32 eight times.

To simplify the left side we just throw away the 1, because X÷1 = X 

Now we have X = 3/8

The answer is 3/8" on paper is equal to 12" in real life

To check our answer we could ask how many of those 3/8s are there in 12 inches?
One way to do this is to convert 3/8 to a decimal number.
Divide 8 into 1.00 and you get .125 then multiply by 3 and you have .375
Now we do the division 12 ÷ .375 = 32 which is where we started (1 inch equals 32 inches)

Whew! Why go through such complications? Why not scale 1:10 or something simple? Well, we use this scale because you can show a typical room or two of a house on one piece of paper.

Q2. Assume an inch of margin on all sides of a sheet of 8 1/2" x 11" paper. What is the largest room that can be drawn on this paper at 1:32 scale? Round the answer to the nearest foot.

A2. Subtract the margins to find remaining space, and calculate the largest scaled room that will fit.

(8.5 - 2 = 6.5) and (11-2 = 9) so 6.5 inches x 9 inches is the free space for drawing a room.

6.5 x 32 (our scale) = 208 inches       Divide 208 ÷ 12 = 17 feet 4 inches which we round to 17

9 x 32 = 288 inches     Divide 288 ÷ 12 = 24 feet 0 inches

The largest room that will fit on this paper is 17 x 24 feet.

Thursday, July 15, 2010

Drawing to Scale, Part 1

Scale drawings save us lots of time and money, but require a bit of math. Here's a sample drawing of a kitchen, with breakfast room and laundry.

Your reaction is likely to be, It's too small! Can we have another?
OK, here's another drawing.

Now you say, It's too big! We've zoomed in too far! 
 Trying one more time - this one is just about right:

Obviously this is not a full-size drawing, because that would be too big to use. We use the concept of scaling to produce an optimally-sized, smaller drawing - big enough to see, handy to print, etc.

This concept of scaling is simple, but gets complicated very quickly. If you know about image types, you can see I made these from a vector drawing program that is designed to scale things up and down. A raster image program spreads pixels apart and the image deteriorates when you zoom in and out.

Now here's the math question:

Q1. Can you tell what scale we have drawn this kitchen?
A1. No and yes. 

I cannot tell just from looking at it on the screen. Some dimensions are shown on it, so I can imagine what the real room is like.

In the center drawing, the TRAYS space is labeled 12. I presume that means the space will be 12 inches wide "in the real world".

In the bottom drawing the breakfast table is marked 36 x 48, so it's 3 feet by 4 feet. I can imagine this because I have eaten breakfast at tables that seat 4 people. But I can't tell the scale yet because I don't know the size of the drawing in the real world.

How can I get a better idea of the size of this? Here's another version. Does it add anything?

Yes, this helps because I have printed the drawing out on a 8 1/2 x 11" sheet of paper. (Trust me, I printed it at its actual size.) We can now compare the actual drawing to a known dimension.

Now I have taped my transparent ruler onto the drawing, over the table. The 48" dimension is equal to 1.5" on the ruler. The drawing scale is 1.5 divided by 48 which can be simplified to 1:32.

Each inch on the drawing is equal to 32 inches in this kitchen.

Another way of describing this scale would be to give the number (or fraction) of inches on the page that equal a foot in the real kitchen.

So if 1 inch = 32 inches, what value X = 12 inches?  Tomorrow we'll give you the answers.

Wednesday, July 14, 2010

In which of these 3 groups do you belong?

Ready? Here it comes - 

There are three types of people in the world: those who can count and those who can't.

Ha ha ha!

Apparently some mathematicians think the world can be divided into three groups:

1. The first group is a set of people who can't count to twenty without taking off their shoes (Artists?) 

These people exist completely apart from math and numbers - numbers simply aren't part of their consciousness. They don't buy into the mystique of math. They easily say, and sincerely mean, numbers don't measure anything significant. Do you fall into this camp? Are you skeptical about math?

2. The second (Business people?) consists of those for whom math works.

Even if they're not mathematicians, math works for them. It does useful things. They may say that numbers don't measure everything, but that's like saying if cars can't take you everywhere, then where they can't go you don't want to go. This group expects math to measure everything significant. Are you a manager or company owner? Do spreadsheets reveal all?

3. The third group (Scientists?) know math inside and out; so well that they know math's limitations. 

They also say numbers don't measure everything, knowing what things they can use numbers to measure, and why. They're not thinking math is invincible, or omniscient, or a miracle-working black art. They use it regularly so they know its shortcomings.

Even though the scientists and the artists represent opposite extremes of mathematical competence, they both know there are things numbers can't measure.

In general, the second, middle group tends to expect (and desire) numbers to be more reliable than they are, and to do more good that they can.

So what do you think? Into which group do you fall? How much do you trust math? And why? 

I can remember years ago there was a saying that PC people did great reports - all the numbers made sense - but Mac people did lovely reports with lots of color, graphs and charts. The poor people with only pencil and paper were at a disadvantage in presentations, but it didn't mean they were at a disadvantage in thinking things through!

Tuesday, July 13, 2010

Parlez-vous mathématiques?

Some of us will know what Parlez-vous français? means. It's Do you speak French? In French.

Today's blog title is prompted by the Tour de France every morning. The commentary is in English, but there's plenty of French being spoken (and seen) on the show. We are traveling through France along with the bicycle racers, and we are about to come up on Bastille Day tomorrow.

I don't speak French very well. I have traveled a lot in France - visiting at least 15-20 times for business and pleasure. I can read fairly well and communicate if I have to - especially about food, cars, and bicycles. But this modest level of competence came at a price. On my first visit I went for weeks not being able to read or speak without serious concentration. My brain was constantly tired.

What does this have to do with math? you ask. This - if you think of math as a language, most of us are in the same position I am with French. We can communicate just a little. We might be able to fool a few people once in awhile. But then we come across REAL MATH language. For example:

In selected trials (n=65,229) patients were followed for  244,000 person-years. Of  2,793 deaths, 1,447 deaths occurred among placebo patients (n=32,606) and 1,346 deaths occurred among patients treated with a statin (n=32,623). The RR for all-cause mortality associated with statins was 0.91 (95% CI, 0.83-1.01). Researchers reported no statistical evidence of heterogeneity between studies (I²=23%; 95% CI, 0%-61%).

Ok, maybe that wasn't so hard. How about this passage:

Compiled 23 studies on the effect of reduced-function cytochrome P450 2C19*2 (CYP2C19*2) genetic variant (n=11,959 participants) and the effect of proton pump inhibitor co-administration (n=48,674). 

The carriers of the loss-of-function CYP2C19*2 allele (n=3,418) had a 30% increased risk for a major adverse coronary event vs. non-carriers (9.7% vs. 7.8%; OR=1.29; 95% CI, 1.12-1.49). This variant was also associated with an increased risk for mortality (1.8% vs.1%; OR=1.79; 95% CI, 1.10-2.91; n=6,225) and stent thrombosis (2.9% vs. 0.9%; OR=3.45; 95% CI, 2.14-5.57; n=4,905).

Proton pump inhibitor users( n=19,614) displayed increased risk for major adverse coronary events (21.8% vs. 16.7%;OR=1.41; 95% CI, 1.34-1.48) and mortality (12.7% vs. 7.4%; OR=1.18; 95% CI,1.07-1.30) versus non-users.

Is this math or gibberish? In any case, it scares us. I present this argument from Jonathan Hayward, a doctoral mathematics graduate/geek:

Most people are taught something horrid as basic math and they later avoid it as much as they can. They don't know what most mathematicians really do is enjoy an art form guided by intuition. Most people think mathematicians must do more of whatever they suffered through in math classes. It's really sad because higher math is easier than lower math!

This author makes the argument that higher math is fun! It's exercising an art form guided by intuition. Here are some mathematicians from MIT. Do they look like they might enjoy math, like these conjectures?

Conjecture:  Let S = (0, 1).  For all x ∈ S there exists y ∈ S such that y > x.
Conjecture:  Let S = (0, 1).  There exists y ∈ S such that for all x ∈ S, y > x.
Conjecture:  Let S = [0, 1].  If  x ∈ S there exists y ∈ S such that y > x.

Professor Dr. Bill Hart appears positively euphoric because his research team discovered answers to:

For which whole numbers n does there exist a square a2 so that a2-n and a2+n are also squares?  

I say, let's stop here, I'm getting a headache. (Why are these guys so often next to a chalk board?)

Monday, July 12, 2010

Too much of a good thing

Value is directly related to Scarcity - in other words, it's possible to have too much of a good thing. Math can help you decide when enough becomes too much.

I saw a great news item today - "Hospital Chef unearths hoard of 52,500 Roman coins!"

Here's an image from the British Museum. 

Roger Bland, a coins expert at the British Museum, said: "The hoard weighs 160 kilos, and it wasn't  easy to recover the coins from the ground. The only way would have been the way the archaeologists had to get them out, by smashing the pot that held them and scooping them out."

Here's a link to a great summary of the find.

Mr. Bland, who encourages metal detector fans to report all their finds, said the hoard had already absorbed more than 1,000 hours of work from his staff. He admitted his stunned reaction when he saw the coins was "Oh my gosh! How are we going to deal with this?" He now says, "the research will keep me going until my retirement." I loved this story. It's a bit like finding the largest gold nugget that we discussed a couple weeks ago.


The coin find reminded me of what a curator at the Page Museum (La Brea Tar Pits) told me a few years ago. They found a new pit full of bones when they were digging out a parking garage nearby.

"Oh No!, what are we going to do with all of this? We already have a million bones, about 250 species EACH of vertebrates and invertebrates PLUS hundreds of plants - maybe three million items. And now all this! We'll need more warehouses! More volunteers. More money. Oh No!"

Go here if you want to see what they are dealing with.


The Chinese museums probably had the same reaction when the Terra Cotta warriers were discovered. Ten warriors are great. Tens of thousands are a problem!


This is the definitely the same response we got from a Greek tour guide when my wife asked why they hadn't completely excavated an interesting cave: "Oh we will eventually. It's probably worked its way up to number 11,000 on our list - all waiting for funding!"

Friday, July 9, 2010


Words again. Yesterday I described how we work with kids so they can clearly describe a problem and clearly state their answers. This is above and beyond understanding the concepts, devising an approach to solve the question, and calculating the answer.

It's the greatest challenge for me when editing math questions - how do we best state the problem. Sometimes we publish a book, get confused readers calling in, and have to change the problems.

For example, in the blog two days ago, I asked, "Q2. How much larger is the copper sphere than the rubber sphere?"

My wife asked, The copper one is smaller, so shouldn't you reword the question to "How much smaller"?

To which I replied, Yes it's smaller but I don't want to tell them that. That gives away the strategy and changes the answer. Let them look at the measurements, figure out a strategy for comparisons, and tell me it's 7/10ths as large.

Of course we can't control whether they pay attention while reading - the teacher is there to help them.

Here are some descriptions extracted from one of our long story problems in the Fourth Grade:

The answer to almost any problem built on this story could be "It depends." We didn't clearly describe the bone count in the skull/face. We did correctly note that the number of bones changes as you grow older and they fuse into fewer, larger bones.

From a technical point of view, this is a very challenging passage to proofread. You would really have to know your skeleton facts to be sure we described things correctly. Did you notice the typographical error in there? I created it on purpose just to see if you would notice. There are a couple format inconsistencies too.

Speaking of noticing, yesterday I changed the background color of the blog from blue to beige. I don't like it so I am changing it back!

Thursday, July 8, 2010

Worthwhile work with words

The last blog was pretty heavy so I think this will be light-weight math.

Language is a very important component of math education. We need to precisely define what we are talking about so we can make comparisons and decisions. Here's an example:

Sides and corners, straight and curved. Simple? Now it gets more difficult (if you are in kindergarten):

We ask them to think about these things and let them make similar objects. They learn to distinguish between physical things (tangible, in their hands stuff) and abstract concepts (straight, curved).

We help kids learn to express what they observe, and to articulate it correctly. Techniques like repeating the questions to assure themselves that they heard it correctly. Answering with a yes or no, and why they came to that conclusion.  Giving the answer with the proper units when units are requested in the question.

Words are all in a day's work for a math student, and for a math curriculum editor.

Wednesday, July 7, 2010

Relative Spherical Density

I noticed the blog yesterday primarily dealt with 3-dimensional objects known as spheres, rather than 2-dimensional shapes known as circles. Titling it "Going around in circles" was misleading. Sorry. But let's not give up on the subject yet. Did you notice the items weighed different amounts even if they were of similar sizes? That means their density varied. Today we calculate relative spherical density.

Here are a few spheres that are NOT sporting equipment. The one on the left is made of solid copper. The one on the right is foam rubber - I squeeze it to give my fingers some relief from too much typing.

Following yesterday's formula, here are the relevant dimensions:

Copper Sphere 5cm diameter  600g weight  &  Rubber Sphere 7cm diameter  30g weight.

We can compare these two objects by multiplying and dividing their dimensions.

In Excel Math we teach elementary school kids how to demonstrate comparisons - for example:

Q1. How much larger is the rubber sphere than the copper sphere?

A1. We divide 7 by 5 and learn that the rubber sphere is 1.4 times as large ( 7cm ÷ 5cm = 1.4 )

Q2. How much larger is the copper sphere than the rubber sphere?

A2. It's ( 5cm ÷ 7cm = .7 ) or seven-tenths as large.

Q3. How much heavier is the copper sphere than the rubber sphere?

A3. ( 600g ÷ 30g = 20 ) so the copper sphere is 20 times heavier than the rubber.

Notice that in all these answers the units disappear. A comparison does not have units!

Q4. For a given volume, how much heavier is copper than foam rubber?

A4. This is much more complex! The formula for volume of a sphere is 4/3 π r³. 
In words, it's four thirds times pi times the radius cubed (multiplied by itself 3 times)

The radius of a sphere is half the diameter so we could end up with something like this:

(4 ÷ 3) x 3.14 x ( d ÷ 2) x ( d ÷ 2) x ( d ÷ 2)

We have to calculate both copper and rubber, so to save time we can do this 4/3π stuff only once and get a "constant value" to use whenever we calculate spherical volume. (4 ÷ 3) x 3.14 = 4.19

4.19 x (2.5 x 2.5 x 2.5) = (4.19 x 15.625) = 65 cubic centimeters
4.19 x (3.5 x 3.5 x 3.5) = (4.19 x 42.875) = 180 cubic centimeters

Excuse me, what was the question again? Oh yes, relative density (mass or weight per unit of volume)

600 ÷ 65 =  9.23 grams per cc
  30 ÷ 180 = .1666 grams per cc

Now we can calculate the answer:

9.23 ÷ .1666 = 55      Copper is 55 times heavier than rubber for the same volume 
(any volume is 55 times heavier - the units disappear).

Tuesday, July 6, 2010

Going around in circles

It was the 4th of July holiday - Independence Day - this weekend. My head was spinning. People were running around kicking, hitting, rolling, batting, etc. The weather is usually good in summer, and we find ourselves outside playing sports and games. Many of these activities include a ball, or sphere.

You probably know most kinds of sports balls, but have you ever compared their mathematical details?

(Yes, I know a shot is not a ball and 10-pin bowling is not done outside)

Balls are described as having a certain diameter or circumference. And usually the weight and material are controlled as well. You can compare these specifications with the image I created here.

Some balls, like volleyballs and soccer balls, are made of panels sewn together. These and other balls that are hollow may be inflated to a certain size or firmness. In the case of these balls the inflation pressures might be specified by the sport authorities.

The balls used in some other sports, like American football and rugby are not round, so I have not included them here.

You also might see another kind of round, circular object at this time of the year: the wheels on the bicycles ridden in the Tour de France.

Wheels are measured in diameter. The rims are a certain width and depth. We count the spokes too.

Bike wheels are a specialized business, and the "big boys" in the business have been at it for a long time. I used to run a bike shop back in the 'Seventies and I got parts from the same people that are still fixing bikes today.

To finish this off, here are some other spherical objects I saw over the weekend.

Friday, July 2, 2010

Blowing off steam

Yesterday we focused on making hot water. Today, we look at the energy required to get water heated up to drinkable temperature.

We heat water by adding energy to it. Water has the ability to absorb lots of energy before it changes state into a vapor (boils and becomes steam).  This is not a science class, just a list of ways to warm up water:
  1. gas-burning water heater
  2. pot on gas stove
  3. electric resistance heater
  4. heat pump that takes heat from the air or ground and transfers it to water
  5. kettle with resistance elements
  6. electric shower heater
  7. microwave oven
  8. solar water heater outside the house (short video)
  9. pan on wood or coal fire
  10. heat collector attached to fireplace or wood stove
In researching this I found some fascinating references and articles. Here's one. What they say is, Don't heat water with your wood stove if you want to remain safe, insured, and clean. If you get something wrong, all that energy you put into the water will come right back at you!

Here's an example of the power of steam - it blew this wood stove apart. I found another story about a guy out in the country who drew water from a well into a firebox heated with his wood stove. When steam pressure built up, it exceeded his expectations, went backwards down his system and blew up the well.

Not this much steam, but you get the idea!

Back to the energy. Yesterday Chris heated 400 ml of water to a boil. He said that required .05 kwhr of electricity.

Q1. How many calories does it take to heat 400 ml of water to 80 degrees C?
You need 1 calorie to raise 1 gm of water 1 degree C. One milliliter of water is one gram.

Chris' 400 ml of water requires 400 calories to warm up 1 degree C.

Assuming his tap water is about 16 degrees C, we raise the water 64 degrees to make his green tea with 80 degrees C water.  (For a detailed explanation of heating water, see this site)

A1. 400 x 64 = 25,600 calories of heat must be added to the water to get it to 80 degrees C.

 My tea mug is filled almost to the brim with 400 ml of cold water.

Q2. How many more calories will it take to get the 400 ml water to 100 degrees (boiling)?

A2. 400 x 20 = 8000 more calories must be added to get water from 80 to 100 degrees C.

Q3. How many calories does it take to turn that amount of at-the-boil water into steam?

It takes a huge amount of energy! You need to add 540 calories per gram.

A3.  400 x 540 = 216,000 calories to turn 400 ml of water into steam (after it is boiling).
All that energy is itching to get out and do some work, so be careful!

    Thursday, July 1, 2010

    We're all in hot water

    Having hot water is one sign of civilization. We like the comfort of a hot shower, a hot bath, and a hot cup of coffee or tea. But since not everyone has this luxury we should be considerate in our energy usage.  I can't imagine an illustrated blog of saving hot water in the shower, so let's look at the cost of hot water for a daily cup of caffeine.

    My friend Chris reports this from the UK:

    Got round to retrieving the energy reading do-dah from the lounge this morning and stuck it in-between the new variable-temp kettle and the socket. A bit rough and ready, I know.

    We used .05 kilowatt/ hrs electricity to heat 400 ml of tap-temperature water to 100 C (boiling!) for black tea. We later used only .03 Kw/hr to heat the same amount of tap water to 80 C for green tea.

    The .02 kwh difference we save is equal to 20 watt/hr. 

    As we use 11w energy save bulbs for background lighting, this means that for every cup of green tea I drink (rather than black tea) we can light a bulb for nearly 2 hours for free!

    Can we save the world by all drinking green tea?  Or perhaps even shift to white tea which only needs 65 degrees?

    What do you think? Could we save the world? What would we need to know to decide?
    • How much tea do people drink?
    • How much energy is consumed heating the water?
    • What means are employed for boiling? ( electricity, gas, wood fire, etc.)

    • Can we measure the energy used boiling all the water? (different than the energy the water needs, because lots can be lost in the process)
    • Does it make any difference that Chris' voltage is 240 while ours is 110?

    • What efficiency gains could be attained in the boiling? (could we save energy)
    • Cost if we all move to the most efficient boiling process (tea kettle, microwaving a cup, etc.)
    • What gains could we get going to green tea? (Chris suggests 40% savings from his one test)
    • Is there an additional cost or savings in making green tea that we can add to the equation?
    • White tea is very rare; would there be enough if we all decided to start drinking it?

    • What would we do with all the extra energy saved?
    • How could we save the world with this energy?
    • What will I do with the white tea leaves because there is no strainer in the cup? 
               (I forgot to put it in while taking the photo!)

    A. Sometimes MATH means knowing a question is too complex to be answered!