... angles severally equal and the sides about the equal angles proportional. The Proof From the given triangle ABC which has a right angle of BAC, a perpendicular AD is drawn from point A to point B. Now because angle A is a right angle like angle BDA, and the angle B is common to ... listed below. The meanings explain their unique purposes in relation to one another. Let's explore how Euclid defines comparison and ratio of like figures. Perpendicular - This occurs when a given line is cut at a point by another line creating two parts and also two right angles. Equiangular - When ... the ...

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... use calculators during tests have no mathematical concept of the criteria given to them. In order to make sure a math problem is sufficiently precise, a calculator is a common tool used to "double-check" the answer for the problem. On a math test, there may be several difficult problems that ... using calculators on tests due to their lack of understanding of the mathematical concepts is unwarranted. Since tests are mostly based on precision, the calculator is a common tool used to demonstrate precision. Most students are incapable of being a hundred percent accurate; if the student is n...

• Word Count: 517
• Approx Pages: 2
• Grade Level: Undergraduate

... use calculators during tests have no mathematical concept of the criteria given to them. In order to make sure a math problem is sufficiently precise, a calculator is a common tool used to "double-check" the answer for the problem. On a math test, there may be several difficult problems that ... using calculators on tests due to their lack of understanding of the mathematical concepts is unwarranted. Since tests are mostly based on precision, the calculator is a common tool used to demonstrate precision. Most students are incapable of being a hundred percent accurate; if the student is n...

• Word Count: 523
• Approx Pages: 2
• Grade Level: Undergraduate

... the x -value of the first point from the x-value of the second point. This will be the "run". For the example points, the slope is one. Parallel and Perpendicular Lines For parallel and perpendicular lines, the slopes have to be in certain relation to each other. To get a parallel line, the slopes of two lines have to be the same. Yes, that ... 's all! If the slopes of two lines are two, then they are both parallel. On the other hand for perpendicular lines the slopes have to be total opposites. If one line has a slope of two, then the slope of a line perpendicular to it would be the rec...

• Word Count: 1169
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• Grade Level: High School

... those things end up being positive. If you take a vote the majority of the students would prefer calculators over a pencil, paper, and the use of their brains. First of all, a calculator saves time by allowing a student to answer a problem faster. The reason of this, is because, if a teacher assign a student about twenty to thirty minutes to complete only thirty problems the ... and multiply, divide, or convert it into a smaller number quicker and easier. By contrasting the mind of a student and a chip of calculator, a calculator thinks a hard problem is easy while we are thinking it is...

• Word Count: 396
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• Grade Level: High School

... use the punch cards as a means for data processing until the 1960's. Following years, couple of engineers made significant advances. One of them was Vannevar Bush (1890 - 1974) who developed a calculator for solving differential equation in 1931. The machine could solve complex differential equations but it was cumbersome due to its hundreds of gears and shafts in order to represent numbers ... and their relationships. To eliminate the bulkiness of Vannevar's calculator, a professor (John V. Atanasoff) and his graduate student (Clifford Berry) envisioned an all-electronic computer that a...

• Word Count: 2409
• Approx Pages: 10
• Grade Level: High School

... times greater in the plane of the graphite rings than at right angles to this plane: (parallel)/(perpendicular) = 106 . Correspondingly, the conductivity of stretchoriented polyacetylene is some 100 times higher in the stretch direction than perpendicular to it. The smaller 4 anisotropy compared to graphite, i.e. non-vanishing(perpendicular), could suggest -short-circuiting- across the chains. Since the polyacetylene chains are not infinite, contacts between ... not the counter ions, I3 - or Na+, but the charges on the polymer that are the mobile charge carriers (see Mechanism of polyme...

• Word Count: 6720
• Approx Pages: 27
• Grade Level: High School

... machine was finally reconstructed in working fashion in 1960. It was however, in 1642 that Blaise Pascal was credited for building the first commercial calculator, a hand powered adding machine, the Pascaline. Although it was more limited than the calculating clock it became better known. It was then ... were several multiplying calculators built each a little different and a little better. It was in 1889 that Dorr E. Felt built the first printing desk calculator. Then came the 1890 US census which was projected to take more than 10 years to tabulate thus running into another census peri...

• Word Count: 976
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• Grade Level: High School

... you have to use these math facts rapidly on the fly "(Yermish, 2011). Calculators are not effective when factoring quadratic equations. How does a calculator help you to determine what two numbers multiply to one number yet add up to another? Automaticity of facts frees up working memory to work ... ) on reading individual words " (Yermish, 2011). Regardless of the amount of time (which is thought to be very little) it takes to use a calculator, those few seconds cause a child to lose track of thought. Though useful, calculators cannot replace the best, most effective tool children have,...

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... it could not have come any sooner, but I didn't mind I knew I was ready for this test. I had all the materials I needed three sharpen pencils, calculator, and my brain. As I sat patiently waiting for my math teacher to pass out the test, I began to repeat formulas and steps in my head. My ... a rush I wrote down the answer and the same with the second problem. When I came upon a more difficult problem I turned to my calculator for the answer, I typed the numbers but something wasn't quite right, I punched in the numbers again and nothing was showing up, my ... calculator had gone dead. ...

• Word Count: 453
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• Grade Level: High School

... in buildings generally different from their original contexts Synagogue: a Jewish house of worship Torah: first five books of the Old Testament traditionally ascribed to Moses Transept: an aisle in a church perpendicular to the nave, where the clergy originally stood BYZANTINE ART Early Byzantine Saint Michael the Archangel 174 324 6th C One leaf of an ivory diptych. It was meant to be ... cases forming a web-like design Tapestry: a woven product in which the design and the backing are produced at the same time on a device called a loom Transept: an aisle in a church perpendicular to th...

• Word Count: 10708
• Approx Pages: 43
• Grade Level: High School

... spread his feet apart so that there was equal weight distributed on the feet. The patient's arms were both on the lateral side of the body. The central ray was perpendicular to the center of the image receptor and entering to one inch inferior to coracoid process. The patient's left arm was rotated externally with the hand supinated. This was done ... spread his feet apart so that there was equal weight distributed on the feet. The patient's arms were both on the lateral side of the body. The central ray was perpendicular to the center of the image receptor and entering to one inch infe...

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• Grade Level: High School

... this. This instrument is about 20 feet long and consists of a straight plank with a five-foot channel for water in the center. Each end of the chorobates had a leg positioned perpendicular to the plank. Plumb bobs at either end shown that the device was level when lined up with vertical lines drawn on the diagonal cross planks. The water in the ... a layer of concrete followed by more mortar and so on. When the foundation was complete, the real construction began. Each wall and pier of the building had to be exactly perpendicular to the foundation. This was achieved using an Egyptian de...

• Word Count: 2911
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• Has Bibliography
• Grade Level: High School

... raised" (Hamilton). There were also square pianos in which the strings ran from left to right as on the clavichord. And by 1800, there were upright pianos whose strings ran perpendicular to the keyboard. The dulcimer, the earliest ancestor of the piano, originated shortly after the birth of Christ, in Iran. The basic principles of the piano were illustrated on this ... a German man names Christian Ernst Friederici in 1745. The pyramid piano was the same design of the grand piano copied to vertical form. This made the strings and soundboard mounted perpendicular to the keys, so that they...

• Word Count: 3032
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• Grade Level: High School

... calculators (29%) or than the combined use of both computer and graphing calculators (10%). Furthermore, the most widely used CAS in the corpus is the graphing calculator (83 papers), followed by Maple (53) and Mathematica (43). Derive (21) and Matlab (11) are also common, as well as 27 papers ... an algorithm efficient for computation and not necessarily one that matches a hand technique. For example, Holm (2003, p. 2) found that an online integral calculator would (rather than using the substitution method for simply expand the product and use the power rule. He notes that such cases ...

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• Has Bibliography

... rack holding two horizontal wires with beads strung across them. Several different types of arithmetic operations could be performed when these beads were manipulated. Another early calculator, later called Napier's Bones, made its debut in the early 1600's. This device, invented by Charles Napier, consisted of a series of rods that ... digital apparatus that could not only add, but could also multiply. It was not until 1820 that a mechanical calculator, developed by Charles Xavier Thomas, was introduced that could perform all four basic arithmetic operations. While Thomas was busy creat...

• Word Count: 7384
• Approx Pages: 30
• Grade Level: High School

... now able to fit in the palm of your hands. Also calculators are able to do a lot more complicated problems today, and display them on much larger screens (example: graphic calculator) One of the early calculating tools were called "The Abacus". It was a simple instrument for working on math problems. It was used by many cultures and dates back to ancient ... man called William Oughtred invented it in the early 1600's. The slide rule made multiplication and division much easier. Engineers and scientists used the slide rules until the invention of calculator in the early 1970's. Until the...

• Word Count: 310
• Approx Pages: 1
• Grade Level: High School

... classes. Most classes require textbooks and additional material to be purchased. For a class like Algebra, a graphing calculator is required. The tablet would be the single source for all the students information. Instead of buying a calculator, the tablet has a application that has the same functions as a graphing calculator. There are thousands of applications and books available that would save the student time and money ... ...

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... pound at the butcher's shop. Regardless of the great cost and effort that went into the making of tables they were inevitably full of errors. The Arithmometer was like a desktop calculator or a cash register and proved to the people there was a need to change the way things were done, an easier way to get the job done, quicker and more efficient ... of inertia and stress distributions. Without the help of these calculations it would not have been possible to build bridges, railroads, steamships or textile mills. The Electronic Numerical Integrator and Calculator (ENIAC) was produced at ...

• Word Count: 2656
• Approx Pages: 11
• Has Bibliography
• Grade Level: High School

... , 1997). Gottfried Leibnitz and Blaise Pascal were the next two people in the history of artificial intelligence. Pascal was 19 years old in 1642 when he invented an eight-digit calculator, the Pascaline. (Mechanical Calculator, n.d.). In 1694 Gottfried Liebnitz invented the Liebnitz Computer, which multiplied by repetitive addition, an algorithm still in use today. Leibnitz also conceived of a reasoning ... calculator for interpreting an evaluating concepts. (Step Reckoner, n.d.) Jumping forward a few hundred years to Joseph-Marie Jacquard. In 1805 Jacquard invented the first truly prog...

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• Grade Level: High School

... ideas). Professional influences: Its emphasis is back to the basics, the 3 R's were emphasized (reading, writing, and arithmetic). Technological Influences: In the math class there should be at least a calculator. Language influences: Language is a part of the whole thinking process. Students verbalize, it is used in problem solving, and relationships are formed. Societal influences: A number of societal factors influence decisions ... a bit of pre-planning. Calculators The use of calculators ensures that the experiences in math matches reality, development of reasoning skills, promote u...

• Word Count: 5657
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• Grade Level: High School

... to programming rules memory. The abacus made an idea for created a computer. Blaise Pascal was the one the credit for building the first digital computer. He invented the numerical wheel calculator that adds entered with dials to help his father with his duties. Pascaline also created by him which used eight movable dials to add sum up to eight figures long ... Leibniz invented a computer that had a special step system gear mechanism for the addend digit, and it was build in the 1694. When Thomas of Colmas created the first successful mechanical calculator that could add, subtract, mult...

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... nearly 12 centuries for the next remarkable advance in computing to appear. In 1642, Blaise Pascal (1623-1662), the 18-year-old son of a French tax collector, invented a numerical wheel calculator to help his father at work. This rectangular box, also called a Pascaline, used eight movable dials to add sums up to eight figures long. The weakness of Pascal's device was ... kept secret until decades after the war. It was the American who produced some achievement. Howard H. Aiken (1900-1973), a Harvard engineer working with IBM, succeeded in producing an all-electronic calculator by 1944 ...

• Word Count: 820
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• Grade Level: High School

... ties to the real world and isolates himself in a lonely pulpit to be close to God. Built to Mapple's specifications, the pulpit is extremely tall and "without a stairs, substituting a perpendicular side ladder" (46). The structure of the pulpit is meant to alienate Mapple. When Mapple is out in the city, he is an extremely popular whale man, but once ... he withdraws into the pulpit, he cuts away all connections to his community. The perpendicular ladder of the pulpit simulates "mounting a ship from a boat to sea" (46). Mapple is located on a vessel by himself. Again, going to sea (meta...

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• Grade Level: High School

... for the equivalency point. First, drawing two tangent lines to the flat portions of the pH curve can determine the equivalency point. Next, draw perpendicular lines to the two previous tangent lines. Find the midpoint on the perpendicular lines and then connect them by a line. The point where the line intersects the pH curve is the equivalence point. To find the half ... ...

• Word Count: 1211
• Approx Pages: 5
• Grade Level: High School