Kerry Maxwell and Lindsay Clandfield provide a selection of useful tips and ideas for recognizing grammatical differences between American and British English. Maxwell and Lindsay Clandfield Type: This excellent teaching tool can be played full-screen and gives clear audio examples of the English phoneme set.

Babylonian mathematics refers to any mathematics of the peoples of Mesopotamia modern Iraq from the days of the early Sumerians through the Hellenistic period almost to the dawn of Christianity. The first few hundred years of the second millennium BC Old Babylonian periodand the last few centuries of the first millennium BC Seleucid period.

Later under the Arab EmpireMesopotamia, especially Baghdadonce again became an important center of study for Islamic mathematics. In contrast to the sparsity of sources in Egyptian mathematicsour knowledge of Babylonian mathematics is derived from more than clay tablets unearthed since the s.

Some of these appear to be graded homework. They developed a complex system of metrology from BC. From around BC onwards, the Sumerians wrote multiplication tables on clay tablets and dealt with geometrical exercises and division problems.

The earliest traces of the Babylonian numerals also date back to this period. It is likely the sexagesimal system was chosen because 60 can be evenly divided by 2, 3, 4, 5, 6, 10, 12, 15, 20 and The problem includes a diagram indicating the dimensions of the truncated pyramid. Egyptian mathematics refers to mathematics written in the Egyptian language.

From the Hellenistic periodGreek replaced Egyptian as the written language of Egyptian scholars. Mathematical study in Egypt later continued under the Arab Empire as part of Islamic mathematicswhen Arabic became the written language of Egyptian scholars.

The most extensive Egyptian mathematical text is the Rhind papyrus sometimes also called the Ahmes Papyrus after its authordated to c. In addition to giving area formulas and methods for multiplication, division and working with unit fractions, it also contains evidence of other mathematical knowledge, [27] including composite and prime numbers ; arithmeticgeometric and harmonic means ; and simplistic understandings of both the Sieve of Eratosthenes and perfect number theory namely, that of the number 6.

One problem is considered to be of particular importance because it gives a method for finding the volume of a frustum truncated pyramid. Finally, the Berlin Papyrus c. Greek mathematics The Pythagorean theorem. The Pythagoreans are generally credited with the first proof of the theorem.

Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics. All surviving records of pre-Greek mathematics show the use of inductive reasoning, that is, repeated observations used to establish rules of thumb.

Greek mathematicians, by contrast, used deductive reasoning. The Greeks used logic to derive conclusions from definitions and axioms, and used mathematical rigor to prove them. Although the extent of the influence is disputed, they were probably inspired by Egyptian and Babylonian mathematics.

According to legend, Pythagoras traveled to Egypt to learn mathematics, geometry, and astronomy from Egyptian priests.

Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem.

As a result, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. The Pythagoreans are credited with the first proof of the Pythagorean theorem[38] though the statement of the theorem has a long history, and with the proof of the existence of irrational numbers.

The diagram accompanies Book II, Proposition 5. Though he made no specific technical mathematical discoveries, Aristotle —c.

Although most of the contents of the Elements were already known, Euclid arranged them into a single, coherent logical framework. Euclid also wrote extensively on other subjects, such as conic sectionsopticsspherical geometryand mechanics, but only half of his writings survive.

Around the same time, Eratosthenes of Cyrene c. AD 90—a landmark astronomical treatise whose trigonometric tables would be used by astronomers for the next thousand years. His main work was the Arithmetica, a collection of algebraic problems dealing with exact solutions to determinate and indeterminate equations.

He is known for his hexagon theorem and centroid theoremas well as the Pappus configuration and Pappus graph. His Collection is a major source of knowledge on Greek mathematics as most of it has survived.

The first woman mathematician recorded by history was Hypatia of Alexandria AD —The order of events or steps in a text. Sequence Lessons – Covers kindergarten through sixth grade. Examples: Show the correct order of events from beginning to end in a story. Gwynne's Grammar: The Ultimate Introduction to Grammar and the Writing of Good English [N.M.

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Within these pages. The Purdue University Online Writing Lab serves writers from around the world and the Purdue University Writing Lab helps writers on Purdue's campus. The CCR anchor standards and high school grade-specific standards work in tandem to define college and career readiness expectations—the former providing broad standards, the latter providing additional specificity.

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