Pythagorean_Triples

Pythagorean Triples MAT126: Survey of Mathematical Methods Pythagorean Triples Pythagorean Triples has centuries of history according to the many web sites I have viewed. Pythagorean Triples and can be understood easily if you have the right web site for explanation. To my understanding (3) whole numbers, as in 3-4-5 make up “the sum of the squares of the legs (the two shortest sides) of a right triangle is equal to the square of the hypotenuse (the longest side),” Ryan, M. (n.d.). The two smaller numbers are the 'a' and 'b' (doesn't matter which one is which, 3, 4 or 4, 3) and the biggest number (5) is the 'c'. I will examine two different ways to think about Pythagorean Triples and show examples of each. First we have the basic first three eligible numbers which are {3, 4, 5} that qualify to be a Pythagorean Triple. From these numbers I can create a new Pythagorean Triple by just doubling the three numbers which gives us: 102 = 62 + 82 The second way we can obtain Pythagorean Triples uses three little simple formulas: a = 2xy b = x2 - y2 c = x2 + y2 Choose any value for x and y that you like -- only let the x be larger than the y, to avoid a negative in the b formula. Observe: Let x = 5 and y = 2. This produces a = 2×5×2 b = 52 - 22 c = 52 + 22 = 20 = 25 - 4 = 25 + 4 = 21 = 29 For breakfast, cereal whether hot or cold, is usually an excellent high-quality selection. I chose Kellogg’s Rice Krispies, which is a good fat free choice. The mathematical formula I am using goes as follows: Serving size is 1 ¼ cups (33g) of Kellogg’s Rice Krispies w/ ½ cup skim milk. Going by the nutrition facts on the box of Kellogg’s Rice Krispies there is zero grams of fat in the above measurements of the cereal w/the skim milk. To figure out the fat content, the formula used is: A serving contains 4 grams of fat; 33g of cereal is 1 and 4/29 of an oz. + ½ cup milk is 4oz. Approx. 5oz. x 29 = 145 grams 3.6% fat-grams per serving. (Based on a 2000 cal. diet there is a total of about 65g of fat, which means if we take that fat total of grams and the total servings in the box, which is 340g of cereal equals about 10 servings of cereal and milk. Breakfast To figure out the protein, the formula used is: 4 calories = 1 gram of protein The 33g of cereal has 130 calories and the ½ cup of skim milk has 50 calories. 170 calories = 1 serving Once again, going by the nutrition facts on the box there is 2g of protein in (33g) of cereal, which is one serving and 4g of protein in the ½ cup of skim milk. When we apply the above formula to the sum of protein grams it looks like this: The number of grams of fat multiplied by 4; (4 x 4) = 16 Lunch Second entrée of the day is lunch, which I usually like to have a can of Progresso, Chicken Noodle with White Meat Chicken Soup. We will use the same formula as above to figure 8 oz. multiplied by 29g the total weight of the product equals 232. 5.8% fat-grams per serving. The math formula’s seemed more accurate on the cereal, yet the above information is once again, off of the product. Dinner I usually have a mixed salad of some sort for dinner. I like to eat very light at night-time and often mix greens or leaf of some type with whatever else I have to add, as far as veggies. I am not going to calculate this meal but I would like to say that I believe it is a good idea to eat your lightest meal at night. Learning more about the math of nutrition is always a good thing so I thought picking the three meals of the day can always help a person keep their weight intact and help manage a fit diet if trying to lose weight/body fat. The advantage to learn new knowledge about the meals we eat can be beneficial in many ways, especially if you work a full time position, keeping to a routine and knowing how to work it will help your energy level greatly in the long run. References Ryan, M. (n.d.). Discovering Pythagorean Triples - For Dummies. How-To Help and Videos - For Dummies. Retrieved July 9, 2012, from to/content/discovering- pythagorean-triples.html