Upstairs Library

Little by little we are finally getting the rooms upstairs in better shape. Today, we finished Esh's room and mostly finished the upstairs library. The upstairs library will be great when there are sleepovers. Gravity can let the dogs out and then go back up to the upstairs library with the dogs. We will put a small coffee maker in Esh's bathroom. When the boys wake up one by one then they can go to the downstairs library so the others can sleep in the family room.

Greek Festival

We are celebrating the Greek Festival here. Last night's dinner was soulvaki, gyros, baklava. My favorite is the yahni. Yum, yum yum,

Written in History

We take many things these days as wonderful creations. But in the history books, they will be a footnote. For example, 200 years from now,

The advent of recording and storage devices reached its zenith with ...[1]....



[1] For a period of about 25 years in the latter 1900's there existed an item called a Cassette Tape. This item was used for storing songs, voices and the like. The existence was so short it is hardly worth mentioning
but is included here for completeness.

Foyle's War

The BBC show called Foyle's War is a real gem. It takes place in WW2 England in a town called Hastings. Detective Foyle investigates all kinds of crimes while the country is in the midst of war. The acting is superb as are the plot developments and characterizations. Watch the show if ou can. We are watching the series on DVD and it is very rewarding, rich TV program.

One God, One Wife

Can you believe this whole polygamist thing in Texas? When the adults get on TV they demonstrate the literacy level of six year olds. The educational level of all of the children needs to be tested to make sure that the children are being educated at the appropriate level. Cults like this Later Day Saints sect or extremist Muslim groups are so dangerous, especially to children. The compound should be shut down and the building razed. Polygamy is illegal in the US -- only one wife allowed. But of course, we are talking about Texas.........

Un-Hinging Stonehenge

The last National Geographic magazine had a wonoderful article on Stonehenge and AOL had one this evening. I love archaeology, especially when it is shrouded in mystery.

The show Stonehenge Decoded airs on the National Geographic channel Sunday June 1 at 9, Mon Jun 2 at midnight, Thur Jun 5 at 9, Fri jun 6 at midnight, sun jun 8 at 4PM, Thu Jun 12 at 5 PM.

Enjoy the mystery!

Gas

An interesting thing was pointed out one the news. Since the 1960s car engines have been designed to be more and more efficient. Some cars now even get 30+ mpg. Yet, we consume more gas as we drive so much more.

Taxes

We just got finished paying $3024.52 in local property taxes and the county officials just announced that there will be an increase! What a %$&#! And we will pay again in December. Maybe that is why death and taxes are put in the same sentence when discussing the unavoidable.

Stimulus Check

We got our tax refund and our stimulus checks so we are able to pay the taxes on the cars and the house! Hooray! And the gas I put in my car two days ago was over $4 per gallon. Whaaaaa... Such is life.

Silence

The silence in the house is delicious. Gravity and I both noticed it and enjoyed it. Poor Esh has a crackled, strained voice from all of the talking over so many hours, too. Let the silence sink in and invade!

Yum

Gravity Well During Grad Party

Grad Party Final Evening

Grad Party Lunch

Grad Party Breakfast

75 pieces of bacon and 24 Pillsbury cinnamon twists; OJ and coffee, Need I say more?

Grad Party 2 Nighttime

Bed at 3 AM and awake 7 hours later.

Grad Party In Progress

Dogs and Teen Boys

I haven't mentioned the dogs in connection with the dogs before. Usually when the boys arrive, the dogs are in their room. Then we let them out. After a few minutes of barking, they usually settle down on the coaches and sleep....except for our one stray who must be predominantly a herding dog. Every time one of the boys leaves the table she gets all upset -- how could they be separating from being so nicely organized (herded) around the table! Blasphemy! Right now, they have moved from the dining room to the library so she is circling around on the first floor and has been doing it for a good twenty minutes. What a little darling. Thank you Pearl for keeping the unruly teens so well organized! :-)
-------------------------------
Added at 9:22 PM

I just noticed that sweet Pearl's ears and top of her head are in the very bottom right corner of the picture in the post above!

------------------------------

Added nitght of 5/25

Here is a nice photo of Pearl with one of the boys she kept telling to sit down every time he got up.

Benefits of Teens

So we have all of these guys here right now -- the stupendous six -- and they will be here for about 34 hours. Some can not spend the night due to other obligations, but off and on they will all be here for roughly 34 hours. But it is great. They are old enough that Gravity and I can ignore them! We bought the food but they can fix most of it and serve it to themselves. Two of them can drive so if they need more, they can go out and buy more! In fact, we plan on having them buy Kentucky Fry for all of us tomorrow evening. Ahhh...the benefits to having independent teens.

We Are Public

All of our blogs have gone public for searches so hence no comments allowed.

Mattress Pad The Sequel

As an update on the mattress pad, I love it. I am sleeping so much more soundly than on the old lumpy , bumpy mattress. The smell is indeed reducing. There is an additional problem though...sheet creep. As the pad adds two inches to the mattress depth, every night when I go to bed, I discover that the fitted sheets have crept up at the corners making the bottom sheet really wrinkly! At this point, I think a mattress pad is definitely in Gravity's future but it will have to be accompanied by new sheets, too! I will get a modified version for Esh's college bed as all of the dorm beds are extra long twins.

Gravity's New Friend Needs a New Dress

Gravity's new friend needs a new dress so he is not Internet connecting at the moment. He will get back to everyone as soon as the 64-bit Vista gets replaced by the 32-bit version. Then emailing and blogging will resume.

Another Proof

Prove the converse of the Pythagorean Theorem. That is, assume that triangle ABC is given with a^2 + b^2 = c^2, and prove that triangle ABC is a right triangle.

Assume that points A, B, and C form a triangle. Also assume that the triangle is scalene with measures of the sides being in the proportion of a^2 + b^2 = c^2.

AD1 allows for points P, Q, and R. Definition 4.18 allows for a triangle to be formed by P,Q, and R such that it is a right triangle. Let’s assume that two of the sides, a and b, match the lengths of two sides of triangle ABC, and that the third side is q. According to Theorem 5.18, as triangle PQR is a right triangle, then q^2 = a^2 + b^2.

As c^2 = a^2 + b^2 and q^2 = a^2 + b^2 then q^2 = c^2. As all of the sides for triangles ABC and PQR are congruent, Theorem 5.16 states that they are congruent. If they are congruent triangles, then ABC must also be a right triangle.

Wireless Printing

We have wireless printing and it is fabulous! Without endless cables from our laptops to the printer, we can print from across the room, across the house, up stairs, even out in the yard! We are thinking of setting up a second one too, along with a second wireless server.

Typos

By no means am I a good typist; in fact, I am actually an awful typist. Years ago, I was tested and I came in at a whopping 7 words a minute due to the significant number of errors. So that brings me to typos....

Thank God spell checking programs were developed! But then there are still those typos that slip through. Like "tow" when you mean "two" or "sex" when you mean "six" or..."testes" when you meant to type "tested". "Item" instead of "time".

So, for a final report to a client you want to type:

Based on the six problem solving steps, the employees followed the first two and tested the results over time.

Instead you type:

Based on the sex problem solving steps, the employees followed the first tow and testes the results over item.

And spell check did not find any errors. So much for the professional image!

The Joy Of Computing

So there I was computing on my new laptop when a dialogue box popped up. Inside it it had an "OK" button and absolutely nothing else. Quandary...what should I do? If I clicked it what was I saying okay to? But I could not do anything until I clicked it. I clicked it. Nothing happened. Ah, the joy of computing.

Geometry Problem 2

In a triangle with side lengths 13, 20, and 21, find the length of the altitude (line drawn from the opposite angle across to the opposite side such that it forms two right triangles) drawn to the side of length 21.

Made In Virginia

Many very nice products are made in Virginia, but perhaps are those made by Smithfield are the best. Smithfield has come up with really great packaged pork roasts. They have them packaged in a gazillion flavors (well, maybe a tad bit fewer than that) such as peppercorn (my favorite), mustard, and even a honey one. Just pop them in the oven and an hour later, a yummy meal. Great when served with baked apple!

Geometry Problem 1

You are given a rectangular box with length 6, width 8, and height 24. What is the length of a segment that originates at a corner of the bottom and terminates at the opposite corner of the top?

Mattress Experiment

I bought a new thick, 2 inches, foam pad to top my 24 year old mattress. So far, I would give it rave reviews! There is an odor that is supposed to go away soon that bothers me a bit, but I swear I am sleeping better than I have for years! If we decide that the pad is a good idea then we will order a pad for Gravity's bed and one for college next year for Esh. I'll keep you all updated...

Miss Our B&N

We miss our local Barnes and Noble. The old local one closed in early May and the new local one (it moved across the street) will not open until mid-June. We will have to wait to browse books and sip coffee while we sit in comfortable stuffed chairs. We will wait with anticipation.

Sum of N-gon Angles

Following is the derivation of the formula for determining the number of angle degrees in an n-gon (a polygon of "n" sides). This can also be found on the October Thoughts blog.

All n-gons can be broken down into triangles by creating line segments from a single angle to the points located at other angles (Theorem 3.25). The number of triangles formed can be determined by identifying the number of interior angles and subtracting the two angles located next to the chosen angle (line segments from the chosen angle to these angles would trace the two sides of the chosen angle). The number of sides on an n-gon equals the number of angles; so you can also use the number of sides less two. In other words, the number of interior triangles that can be formed in any n-gon equals the number of sides on the n-gon less two sides.

According to Theorem 4.53, all of the interior angles of a triangle sum to a linear angle which, as shown in earlier problems, is 180. The measure of the angles can be determined by multiplying 180 (per triangle) times the number of sides on the n-gon less two (number of interior triangles). Therefore, if n is the number of sides the following applies:

Number of angle degrees = (n-2)(180)

Gravity Has A New Friend

The old friend was SO loud and independent
It just had to go!
When we watched TV,
It would steal the show.

Needing special air conditioning
All of its own
We decided its use
Had to find a new home.

Bye to the "shock absorbers"
Bye to the loud whine
When it kept shutting off on its own
Was a very clear sign.

So in with the shiny and new
In with the sleek and slim
So quiet now
We miss the din!

Indiana Jones

Last weekend, while all three of us worked on our various computer-based activities, TBS ran all three of the first Indiana Jones movies back-to-back. It was fabulous. Each one is such a delightful romp of humor and adventure. We must go see the fourth one that is about to be released!

Goodwill

Wow, we have a really nice brand new Goodwill store that opened up across from Esh's orthodontist. We dropped off a huge bunch of old shorts, swim trunks, etc. that all looked so tiny compared to Esh's current 6'2" of height and his broad shoulders. My...how fast they grow.

What I Have Been Up To

"Although viewing lengths as numerical quantities is a relatively recent development in geometry, it has caught on quite well and is very much ingrained in the modern view of geometry. The previous chapters are a demonstration that geometry can get along quite well without numbers, and many geometrical ideas can be developed purely geometrically. Also, one obtains a more clear axiomatic development of geometry by asserting only geometric axioms
and avoiding a separate development of the real number system."

This explains it all.

Continuity

I have recently begun to deal with continuity in the mathematical sense. Lines are not supposed to have holes and they are supposed to go on to infinity. But if points have no dimension but are just a location in space, then why doesn't a line have holes? If a line is the distance between two points and it contains an infinite number of points then how can it exist; would its existence be like adding an infinite number of zeros together and getting something?

Proof

Among others, here is a proof I did recently that I like.
---------------------------------
Prove that the diagonals of a rectangle are congruent.

Given that points A, B, C, and D form a rectangle, according to the definition of a rectangle, Definition 4.26, it is a quadrilateral with all of its angles congruent. Theorem 4.97 also states that all of the congruent angles in a rectangle are right angles therefore implying that all consecutive sides are perpendicular. According to Theorem 3.25, diagonals can be formed with segments AC and BD thus forming triangles ABC and BAD.

As all of the consecutive sides are perpendicular, then Theorem 4.67 can be used to show that opposite sides of the rectangle are parallel meaning that quadrilateral ABCD is a parallelogram. Theorem 4.85 states that opposite sides of a parallelogram are congruent; therefore sides DA and BC are congruent and sides AB and CD are congruent. As all angles are congruent and right, then angles ABC and BAD are congruent. At this point, Theorem 4.18 can be used to show that triangles ABC and BAD are congruent. Using Theorem 4.20, the two diagonals can be concluded to be congruent. Therefore, it can be concluded that the diagonals of a rectangle are congruent.
-----------------------------------
Definition 4.26: If all angles of a quadrilateral are congruent then the quadrilateral is a rectangle.

Theorem 4.97: The angles of a rectangle are all right angles.

Theorem 3.25: For any points A and B, both A and B lie on segment AB.

Theorem 4.67: If line l is perpendicular to line m and line m is perpendicular to line n then lines l and n are parallel.

Theorem 4.85: Opposite sides of a parallelogram are congruent.

Theorem 4.18: If points A, B, and C are non-collinear and points P, Q and R are non-collinear, then triangles ABC and PQR are congruent if and only if segments AB and PQ are congruent and segments BC and QR are congruent and angles ABC and PQR are congruent.

Theorem 4.20: If points A, B, and C are non-collinear and Points P, Q, and R are non-collinear, then triangles ABC and PQR are congruent if and only if segments AB and PQ are congruent and segments BC and QR are congruent and segments CA and RP are congruent.

Driver's License In Hand

Tonight, Gravity and Esh went to one of the county's high schools and sat in a packed auditorium so Esh could be handed his actual driver's license! The judge handing out the licenses had quite a sense of humor. According to Gravity and Esh, in the five minute talk to parents, he said that DMV will take away a license for any reason that the parent's feel is appropriate such as "having more holes in your face than you are born with" or "not having enough vowels on your report card". The one bauble in the whole thing is that according to the license, we live on East Bridge Road but there is no East Bridge Road in the entire county (I checked)! But a new license is already ordered.

Mothers Day

Regardless of whether mothers are important every day or not, it is just plain fun to have mothers day. It's fun for the mother and for those who participate. It's an act of kindness and caring.

I just made cinnamon twists and we will do cards later.

It's a day much like any other but wouldn't it be nice to have someone dote over you
and relieve you of some responssibilities - just for a day?

Wisdom

Wisdom can be viewed as having clear vision of the world around a person. Wise words from Einstein:

"Two things are infinite: the universe and human stupidity; and I'm not sure about the universe."

Herding Cats

As I let out the dogs and they all take off into the woods because they smell the deer or something, I feel like I am herding cats trying to get them back in.

It occurred to me that self organization of simple organisms and possibly even particles themselves follow a similar pattern. When an outside observer tryies to "catch" a particle or observe an object, we distrurb it and it takes off in some direction. Hiesenburg's uncertainty principle can come into play here. Or with organisms, it may stimulate the organism to move in a random direction.

However, when left alone, some form of equilibrium tends to occurr. With organisms, there might be a tendency to come together and self organize giving rise over time to complex organisms. With particles, they may tend to form stable atoms and so on.

Toss in evolution and one's that come together in a favorable way, would tend to propogate.

Simplistic examples but it would be interesting to model "cat herding" and compare this with organism and particle behavior.

So I guess if I left the dogs alone, they would come to the back door on their own eventually, probably with a collective intent. However, in the case of dogs, they may have eaten the deer poop, mushrooms and whatever else they can find and get themselves sick.

Natural Painting

In a neighborhood of manicured lawns, perfectly mulched areas and groomed shrubs, we prefer a "natural painting" look.

Are You Shipping Me?

My new favorite ad is for CarMax:

Two men are in a room that appears to be an ancient store with ship models on the shelves. The men are dressed in the era of Columbus but when they begin to talk, they have modern day accents.

"...If I'd like to purchase on the far end of the world would you hold it for me until I can go pick it up?"

"No sir. We will ship it to you."

"You'll ship my ship?"

"We'll ship your ship to any ShipMax in the entire flat world."

"Are you shipping me?"

Salt

Salt is one of the compounds that all animals need in order to be healthy. It helps our bodies maintain homeostasis. Gandhi went on a fast when the British government tried to control salt production. It even has religious significance. Chlorine gas and solid sodium have explosive results when placed together.

Recently, people have switched from refined salt to sea salt as the prefered table condiment. Sea salt is supposed to be less harmful than regular table salt especially for people with high blood pressure. However, there are also drawbacks to using sea salt. Perhaps, one of the main issues with sea salt is that it is not iodized and trace amounts of iodine are required for proper thyroid function. Many people get iodine naturally from fish products. However, people with fish allergies might fall short on iodine if they give up iodized table salt.

Sea salt is simply salt harvested srom the sea. A benefit of this is that several metals that we need in trace amounts are often found in sea salt such as magnesium. A drawback of this natural harvesting is that heavy metals are also sometimes found in sea salt. These can include lead and even traces of radioactive metals that end up in Earth's seas.

For me, I am going to use both iodized refined salt and sea salt. This way I might get the benefits from both salts and reduce the chances of some of the harmful effects.

48 hour marathon of Superfriends

So yesterday was a successful 7 hour campaign. Esh is probably going to have a 48 hour play, sleep and eat D&D marathon with his other "Superfriends", as they have been dubbed, for a graduation celebration.

October (Mrs. Weasley-even the red hair) stuffed them with chips, carrots, strawberries, Dinosaur chicken nuggets, pretzel nuggets, and Milano cookies and milk Saturday.

Imagination...

Perspective

While catching up on my magazine reading, I came across an article that made me take a different perspective on my old drawing and writing friend, the pencil. The article was on garphene (http://www.sciam.com/article.cfm?id=carbon-wonderland). It begins by stating the following:

"Consider the humble pencil. It may come as a surprise to learn that the now common writing instrument at one time topped the list of must have, high-tech gadgets." Interesting perspective.

A Great Author

I have seen the movie 2001: A Space Odyssey that I do not even remember the first time. I love this movie, especially the ending. T me the ending symbolizes Schrodinger's simultaneity theory. If something is in a state that you can not clearly identify, then it is in all states of existence because all states are possible.

March of this year, Arthur C. Clarke died at 90. He made a wonderful mark on the world and he will be missed.