An Introduction to the Pythagorean Theorem

Mathematicians have labored for ages to discover relationships within triangles along with other polygons. One of the famous and beneficial relationships ended up being uncovered by the Greek mathematician called Pythagorus. He found the sides of a right triangle are related in the following way:

When the lengths of each of the shorter two sides (the legs) of the right triangle are squared and the squares added together, the total is the same as the length of the 3rd side (called the hypotenuse) squared. So should you notice a right triangle, keep in mind that the lengths of the 2 smaller sides are related to the length of the longest side.

If an individual had time to form three external squares from each side of any right triangle, you will discover the smaller squares result in an interesting relationship as compared to the big square.

A triangle whose edges measure 3 units, 4 units, and then five units is one of the most well-known triangles in just about all of mathematics. Squaring each of the 2 smaller sides yields nine sixteen Equals 25 sq units. The longer side is five units, which means its square has an area of twenty-five square units. This arrangement holds true for each and every right triangle.

Many problems that deal with right triangles yield decimal answers. However, there are many examples of whole numbers combinations that are possible in right triangles. Some of these are:

three, four, five

six, eight, ten

five, twelve, thirteen

seven, twenty-four, twenty-five

eight, fifteen, seventeen

Each of the above combinations represent the three lengths of a right triangle. In class, teachers often begin to teach the concept of the Pythagorean Theorem using whole number examples. Later in class, many of the answers may contain one or more sides whose lengths are not whole numbers.

In a right triangle, the 2 smaller sides are legs and the longest side is known as a hypotenuse. Usually a stands out as the shorter of the two legs and b is usually the longer of the legs. In some cases, a is the identical length as b. All right triangles contain a lengthiest side that is directly across from the right angle. This longest side is represented by the variable “c” and it is referred to as the hypotenuse.

Frequently, major findings in science and math obtain distinctive names. Since this special relationship within right triangles was unearthed by Pythagorus, it has been referred to as Pythagorean Theorem in his honor.

For more information on the Pythagorean Theorem and other topics, see my website at http://www.freemathresource.com

The Pythagorean Theorem

The Pythagorean Theorem

Museum of Welsh Life

The Museum Of Welsh Life, at St Fagans near Cardiff Wales. National Museum & Gallery and Museum of Welsh Life, take you to the ancient roots of the origin and gradual development of Cardiff life style.

Why This Kolaveri Di

The term Kolaveri appeared as the number one Indian trend on Twitter on the evening of 21.11.2011. Why this Kolaveri di (English: Why this murderous rage, girl) is a song from the new Tamil movie called “three”, due to be brought out in 2012. The song is composed and vocalized by popular Tamil movie star Dhanush. A promotional video this song was brought out on YouTube on sixteenth November 2011, and it at once got viral on social networking sites for its unconventional “Tanglish” (Tamil-English). In this song, the video recording of the song has become the most attractive part video itself. There was a crude telecasting released with this exclusive, which has become a big craze with the net. The promo has the actor-playback singer Dhanush vocalizing the song in a studio apartment, and composer Anirudh at the piano, while wife Aishwarya Rajinikanth and co-star Shruti Hassan looking on along and giving hints.

Dhanush says, it’s a song that is fit for bathroom singers. It’s bare drums make it more appealing. Dhanush’s description of brokenheartedness by Kolaveri Di is exceedingly amusing. Heartbreak is a phenomenon that almost all is aware of and everybody can associate to and has fired the fame of Kolaveri Di. Since its release, the makes has decided to release an official release.

Why This Kolaveri Di

Pseudomonas aeruginosa

In his paper, “Sur les colorations bleue et verte des linges à pansements”, introduced by Louis Pasteur, Carle Gessard describes the isolation of an organism causing a blue-green coloration of wound dressings . He describes this ‘accidental’ organism as colourless, globular, to . thousandths of a millimetre in length, aerobic and very motile. The bacterium was named Bacillus (rod) pyocyaneus. Today we refer to this organism as Pseudomonas aeruginosa. This species is ubiquitous in the biosphere, has wide metabolic versatility and high intrinsic and acquired resistance to antimicrobials. It can be found in a wide variety of ecological environments ranging from fresh and salt water to the rhizosphere in which they colonize the endemic fauna (e.g. nematodes), flora and fungi (e.g. Pythium spp.) . The opportunistic bacterium P. aeruginosa occasionally migrates from its natural environment and causes disease in animals (wild, domestic and livestock) and humans. In the latter it has emerged, partly due to its intrinsic antibiotic resistance, as a major pathogen in the airways of cystic fibrosis (CF) patients, causing often-fatal chronic respiratory infections, and as one of the most clinically significant opportunist nosocomial agents. Immunosuppressed patients such as those with severe burns, cancer or AIDS are particularly at risk.

Numerous research groups have demonstrated that P. aeruginosa clinical isolates are genotypically, chemotaxonomically, and functionally indistinguishable from environmental isolates. Römling et al. observed that the most frequently identified clone in CF patients was also detected at a relatively high frequency in aquatic environments and Rahme et al. demonstrated the infectivity of a P. aeruginosa strain in both plant and animal models . Similarly, P. aeruginosa strains isolated from a gasoline-contaminated aquifer were indistinguishable from clinical isolates and both oil-contaminated soil isolates and clinical isolates showed pathogenic and biodegradative properties.

Population structure

Using multilocus enzyme electrophoresis, Maynard Smith and colleagues demonstrated that bacterial population structures could range from panmictic or fully sexual, with random association between alleles, to clonal, with nonrandom association of alleles, the latter resulting in the frequent recovery of relatively few of the many possible multilocus genotypes . An intermediate type of population structure that is predominantly sexual, but harbours some epidemic clones, which show significant association between loci, was called ‘epidemic’.

The population structure of P. aeruginosa has been the subject of numerous investigations, we present an overview. Both Denamur et al. in , and Picard et al. in , suggested a panmictic population structure for the species but highlighted the need for caution in inferring the population structure from any single class of genetic marker , . In , comparative sequencing of environmental and clinical isolates revealed a net-like population with a high frequency of recombination between isolates . Using randomly amplified polymorphic DNA typing, Ruimy et al. demonstrated that bacteremia and pneumonia were not caused by specific P. aeruginosa clones . In Lomholt and colleagues suggested an epidemic population structure for a P. aeruginosa population isolated mainly from patients with keratitis and their environment . They found evidence for an epidemic clone that is pathogenic to the eye and is characterized by a distinct combination of virulence factors. In , we combined the data obtained by different typing methods, performed on a batch of unrelated clinical and environmental P. aeruginosa isolates, collected across the world and observed a clear mosaicism in the results and a non-congruence between experiments, features of a panmictic population structure . But, in this network we also observed some clonal complexes characterized by an almost identical data set. There was no obvious correlation between these dominant clones and habitat or, with the exception of some recent clones, their geographical origin. Therefore, we suggested an epidemic population structure for P. aeruginosa. Using multi locus sequence typing (MLST), Curran et al. confirmed in that P. aeruginosa exhibits a nonclonal epidemic population structure . The P. aeruginosa population in the River Woluwe in Brussels was found to be almost as diverse as the global population, harbouring members of nearly all successful clonal complexes.

Several groups found that P. aeruginosa possessed a highly conserved genome, which encoded genes important for survival in numerous environments including humans and evolved through the acquisition, loss, and reorganisation of genome islands and genome islets –. Horizontal gene transfer (HGT) might play a more important role than point mutation in the adaptation of P. aeruginosa to different habitats. Despite not believed to be naturally competent, P. aeruginosa displays a high level of interstrain genomic plasticity and contains a high number of unfixed genes. Shen et al. put forward the idea of a population-based supra-genome that is substantially larger than the genome size of any of the component strains . No two strains would be identical in terms of their genetic content and HGT continuously creates new strains with unique genetic characteristics.

Environmentally endemic bacteriophages are probably responsible for a fair amount of HGT, as they were shown to be formidable transducers of naturally occurring microbial communities of P. aeruginosa.

Pirnay J-P, Bilocq F, Pot B, Cornelis P, Zizi M, et al. (2009) Pseudomonas aeruginosa Population Structure Revisited. PLoS ONE 4(11): e7740. doi:10.1371/journal.pone.0007740

Prevent Diabetes with Better Eating Habits

When watching our health, what we eat is just as important as how much we eat. Too many of the wrong tasty treats can be an invitation to diabetes. This is one risk factor for diabetes that is easily eliminated by developing good eating habits.

The body is a machine that needs fuel to run. We are supposed to eat to live, but often we are “living to eat.”  Some of the foods we eat taste good, but are not necessarily good for us. Consuming these foods can result in medical complications and diseases, including diabetes.

The first thing that we can do to prevent diabetes from knocking at our door is learn the right things to eat. If we simply say “eat healthy” you won’t know what we mean by that. You deserve a better explanation, and here it is:

Use the food pyramid. Check out MyPyramid.gov to take a look at the new and improved food pyramid. It goes step-by-step through the different types of food groups: carbohydrates, fruits, vegetables, fats and oils, sweets, and protein. A balanced diet is what your body needs to function at its best. You’ll feel and look better with a properly balanced diet.

Sort out your carbohydrates. There are two types of carbohydrates: simple and complex. Simple carbs are those that don’t offer any nutritional value and we know are bad for our body. These simple carbs include sugary snacks, processed sweets, sweet drinks, and any foods made from refined white flour. The carbs that are good for you are the complex carbs, which are really the good tasting carbs, scout’s honor! Complex carbs include fruits, vegetables, leafy greens, and whole grains.

Learn about the glycemic index. The glycemic index is a way of rating carbohydrates according to how much they spike your blood sugar compared with pure glucose. Any carb that is rated 50 or below is considered “low GI” (glycemic index). Be careful of making assumptions here. Not all good “complex carbs” are “low GI.” For instance, white potatoes are complex carbs but they have a “high GI.”

Choose good proteins. Protein is one of the major building blocks of all cells in your body. It is usually not hard to find enough sources of protein. The problem is finding enough excellent sources of protein. Eat lean meats, seafood, fish, nuts, and  beans such as black beans, pinto beans, navy beans, lentils, and garbanzo beans for your protein boost.

Good oils do exist. Fats are important in the body. They are used in the makeup of cellular membranes and cushioning of the organs and tissues in the body. Healthy fats include unsaturated oils such as olive, canola, and safflower.

Good eating habits often involve emptying your pantry. Don’t set yourself up for failure by keeping around empty calories and bad fat. Make your good diet a priority in your life and ask everyone in your house to respect your decision.

Clean out all the unhealthy foods from your pantry and restock with only healthy choices.

You now have the basic information about what foods to eat and what foods to avoid. Do your homework before you plan your meals and you’ll be well on your way to transforming your eating habits. You’ll also be well on your way to lowering your risk of diabetes.

Amar Akbar Anthony

Amar Akbar Anthony (Produced and Directed by Manmohan Desai) is one of the best Indian movies ever made. The story is slightly different compared to the usual Bollywood movies. Three brothers including the parents are separated at birth. One is found and brought up a Hindu, another Christian cleric and the smallest by a Muslim tailor and raised according their adopted parents. Therefore the eldest becomes a Hindu police officer, the middle son becomes a Muslim tailor and finally the youngest a Christian comic and liquor dealer. The film depicts the descending demographic order; the Hindu (80%), Muslim (15%), and Christian (3%) communities of India living in complete unity, harmony and brotherhood.

Story: Mrs. J. M. Desai and Pushp Raj Sharma;

Screenplay: Prayag Raj;Scenario: K. K. Shukla;

Dialogue: Kader Khan;

Art Director: A. Rangraj;

Editing: Kamalakar;

Director of Photography: Peter Pereira;

Lyrics: Anand Bakshi;

Music: Laxmikant, Pyarelal

The cast of Amar Akbar Anthony

Amitabh Bachchan	.... Anthony
Vinod Khanna	        .... Amar
Rishi Kapoor	        .... Anthony
Parveen Babi	        .... Jenny
Shabana Azmi	        .... Laxmi
Neetu Singh	        .... Salma
Pran	                .... Kishenlal