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	<title>blog.brightstartutors.com &#187; Mathematics History</title>
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	<link>http://brightstartutors.com/blog</link>
	<description>mathematics and physics - learning and enjoying</description>
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		<title>A Gem From Newton&#8217;s Principia</title>
		<link>http://brightstartutors.com/blog/2011/04/26/a-gem-from-newtons-principia/</link>
		<comments>http://brightstartutors.com/blog/2011/04/26/a-gem-from-newtons-principia/#comments</comments>
		<pubDate>Tue, 26 Apr 2011 20:02:59 +0000</pubDate>
		<dc:creator>curiousCharacter</dc:creator>
				<category><![CDATA[Astronomy Mathematics]]></category>
		<category><![CDATA[Mathematics History]]></category>
		<category><![CDATA[Thrilling Math]]></category>

		<guid isPermaLink="false">http://brightstartutors.com/blog/?p=1456</guid>
		<description><![CDATA[Isaac Newton's Mathematica Principia (1687) has been described as the most important, but also the least read, scientific book ever written. It has been little read mostly because it has been little comprehended. The book is filled with complex geometric diagrams, and Newton's explanations are brief, the assumption being that the reader's mathematical knowledge and ability is very high. 
However, there is at least one result that Newton derived in the Principia that is fairly easy to understand, and I will describe it in this post. It also happens to be one of the important theorems in the Principia: a proof that Kepler's Second Law  of planetary motion isa consequence of mechanics.]]></description>
		<wfw:commentRss>http://brightstartutors.com/blog/2011/04/26/a-gem-from-newtons-principia/feed/</wfw:commentRss>
		<slash:comments>1</slash:comments>
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		<title>The Basel Problem</title>
		<link>http://brightstartutors.com/blog/2010/09/29/baselproblem/</link>
		<comments>http://brightstartutors.com/blog/2010/09/29/baselproblem/#comments</comments>
		<pubDate>Wed, 29 Sep 2010 17:12:11 +0000</pubDate>
		<dc:creator>curiousCharacter</dc:creator>
				<category><![CDATA[Euler's Greatest Hits]]></category>
		<category><![CDATA[Mathematics History]]></category>
		<category><![CDATA[Number Theory]]></category>
		<category><![CDATA[Math]]></category>

		<guid isPermaLink="false">http://brightstartutors.com/blog/?p=779</guid>
		<description><![CDATA[The history of mathematics has many instances where someone has posed a problem for the mathematical world at large to solve, and the problem was not resolved for decades, or even centuries. Often, new mathematics has been discovered in the process of working out a solution.
This post is the story of one such case, the so-called Basel Problem, first posed as a challenge to European mathematicians in 1644. It withstood all attempts to solve it until, in 1734, young Leonard Euler found the answer. As the reader will see, Euler's solution is a work of astonishing ingenuity, even though the level of the mathematics does not go beyond Algebra I.]]></description>
		<wfw:commentRss>http://brightstartutors.com/blog/2010/09/29/baselproblem/feed/</wfw:commentRss>
		<slash:comments>4</slash:comments>
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		<title>Pythagorean Triples</title>
		<link>http://brightstartutors.com/blog/2010/07/21/pythagorean-triples/</link>
		<comments>http://brightstartutors.com/blog/2010/07/21/pythagorean-triples/#comments</comments>
		<pubDate>Wed, 21 Jul 2010 17:30:54 +0000</pubDate>
		<dc:creator>curiousCharacter</dc:creator>
				<category><![CDATA[Learning Math]]></category>
		<category><![CDATA[Mathematics History]]></category>
		<category><![CDATA[Number Theory]]></category>

		<guid isPermaLink="false">http://brightstartutors.com/blog/?p=650</guid>
		<description><![CDATA[
When math textbooks need an example of a right triangle, they frequently use a triangle with sides of length 3, 4, and 5, since the numbers work out so nicely: \(3^{2}+4^{2}=5^{2}\) by the Pythagorean theorem. If that gets tiresome, 12, 5, 13 might be used: \(5^{2}+12^{2}=13^{2}\). Clearly, multiplies of these numbers work also, e.g. \(6^{2}+8^{2}=10^{2}\).
Such [...]]]></description>
		<wfw:commentRss>http://brightstartutors.com/blog/2010/07/21/pythagorean-triples/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
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		<title>What is e, and Why is it Important?</title>
		<link>http://brightstartutors.com/blog/2010/03/08/e_part_1/</link>
		<comments>http://brightstartutors.com/blog/2010/03/08/e_part_1/#comments</comments>
		<pubDate>Tue, 09 Mar 2010 02:34:22 +0000</pubDate>
		<dc:creator>curiousCharacter</dc:creator>
				<category><![CDATA[Mathematics History]]></category>
		<category><![CDATA[Trig/PreCalculus]]></category>

		<guid isPermaLink="false">http://brightstartutors.com/blog/?p=446</guid>
		<description><![CDATA[This post is  to give some background about the constant e. Math students normally encounter e (2.7182818284590452…) in their Precalculus chapter on exponentials and logarithms, and they often wonder where this rather odd number comes from, and what is special about it. ]]></description>
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		<slash:comments>2</slash:comments>
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		<title>The Greatest Formula in Mathematics</title>
		<link>http://brightstartutors.com/blog/2010/01/29/the-greatest-formula-in-mathematics/</link>
		<comments>http://brightstartutors.com/blog/2010/01/29/the-greatest-formula-in-mathematics/#comments</comments>
		<pubDate>Sat, 30 Jan 2010 01:52:09 +0000</pubDate>
		<dc:creator>curiousCharacter</dc:creator>
				<category><![CDATA[Euler's Greatest Hits]]></category>
		<category><![CDATA[Mathematics History]]></category>
		<category><![CDATA[Thrilling Math]]></category>
		<category><![CDATA[Math]]></category>

		<guid isPermaLink="false">http://brightstartutors.com/blog/?p=415</guid>
		<description><![CDATA[It’s usually called Euler’s Identity, after the great Swiss mathematician Leonard Euler, and several polls of mathematicians and physicists have bestowed on it titles such as “the greatest equation ever”]]></description>
		<wfw:commentRss>http://brightstartutors.com/blog/2010/01/29/the-greatest-formula-in-mathematics/feed/</wfw:commentRss>
		<slash:comments>16</slash:comments>
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		<title>Newton Verifies the Law of Gravity</title>
		<link>http://brightstartutors.com/blog/2010/01/14/newton-verifies-the-law-of-gravity/</link>
		<comments>http://brightstartutors.com/blog/2010/01/14/newton-verifies-the-law-of-gravity/#comments</comments>
		<pubDate>Thu, 14 Jan 2010 16:20:09 +0000</pubDate>
		<dc:creator>curiousCharacter</dc:creator>
				<category><![CDATA[Mathematics History]]></category>
		<category><![CDATA[Physics]]></category>
		<category><![CDATA[Thrilling Math]]></category>

		<guid isPermaLink="false">http://brightstartutors.com/blog/?p=399</guid>
		<description><![CDATA[Although much of Newton's work is accessible only to specialists, some of his results can be understood and appreciated by the rest of us. In this post I will describe one such investigation – his effort to determine how the force of gravity decreases with distance from the earth. The results were very significant in a scientific sense, and the way he carried out the work shows astonishing insight and imagination.]]></description>
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		<slash:comments>1</slash:comments>
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		<title>How Many Prime Numbers Are There?</title>
		<link>http://brightstartutors.com/blog/2009/11/24/how-many-prime-numbers-are-there/</link>
		<comments>http://brightstartutors.com/blog/2009/11/24/how-many-prime-numbers-are-there/#comments</comments>
		<pubDate>Wed, 25 Nov 2009 00:59:36 +0000</pubDate>
		<dc:creator>curiousCharacter</dc:creator>
				<category><![CDATA[Mathematics History]]></category>
		<category><![CDATA[Number Theory]]></category>
		<category><![CDATA[Thrilling Math]]></category>

		<guid isPermaLink="false">http://brightstartutors.com/blog/2009/11/24/how-many-prime-numbers-are-there/</guid>
		<description><![CDATA[Are there an infinite number of prime numbers? Or maybe there is a largest prime number, and every number after that is composite. To get a little insight into this, we might start listing the prime numbers, beginning 2, 3, 5, 7, 11, …,  to see if any pattern emerges. About all that is [...]]]></description>
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		<slash:comments>1</slash:comments>
		</item>
		<item>
		<title>How Math Ended Signal Distortion</title>
		<link>http://brightstartutors.com/blog/2009/10/03/how-math-ended-signal-distortion/</link>
		<comments>http://brightstartutors.com/blog/2009/10/03/how-math-ended-signal-distortion/#comments</comments>
		<pubDate>Sun, 04 Oct 2009 04:48:01 +0000</pubDate>
		<dc:creator>curiousCharacter</dc:creator>
				<category><![CDATA[Mathematics History]]></category>
		<category><![CDATA[Thrilling Math]]></category>

		<guid isPermaLink="false">http://brightstartutors.com/blog/?p=371</guid>
		<description><![CDATA[On the morning of August 2, 1927, a young electrical engineer named Harold Black was riding the Lakawanna Ferry across the Hudson River on his way to work in Manhattan, where he was employed by Bell Laboratories. Black was pondering an important problem that he had wrestled with for several years without making any progress. [...]]]></description>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Pythagoras and His Theorem</title>
		<link>http://brightstartutors.com/blog/2009/07/02/pythagoras-and-his-theorem/</link>
		<comments>http://brightstartutors.com/blog/2009/07/02/pythagoras-and-his-theorem/#comments</comments>
		<pubDate>Fri, 03 Jul 2009 04:04:52 +0000</pubDate>
		<dc:creator>curiousCharacter</dc:creator>
				<category><![CDATA[Mathematics History]]></category>
		<category><![CDATA[Thrilling Math]]></category>
		<category><![CDATA[Math]]></category>

		<guid isPermaLink="false">http://brightstartutors.com/blog/?p=304</guid>
		<description><![CDATA[One of the most important and famous formulas in mathematics is the Pythagorean Theorem: for a right triangle, the square of the long side (hypotenuse) is equal to the sum of the squares of the other two sides. Using a diagram:

\[ a^{2}+ b^{2}= c^{2}\]
As I have pointed out in other posts, proofs of major results [...]]]></description>
		<wfw:commentRss>http://brightstartutors.com/blog/2009/07/02/pythagoras-and-his-theorem/feed/</wfw:commentRss>
		<slash:comments>2</slash:comments>
		</item>
		<item>
		<title>Where does pi R squared come from?</title>
		<link>http://brightstartutors.com/blog/2009/06/29/where-does-pi-r-squared-come-from/</link>
		<comments>http://brightstartutors.com/blog/2009/06/29/where-does-pi-r-squared-come-from/#comments</comments>
		<pubDate>Mon, 29 Jun 2009 05:51:02 +0000</pubDate>
		<dc:creator>curiousCharacter</dc:creator>
				<category><![CDATA[Mathematics History]]></category>
		<category><![CDATA[Thrilling Math]]></category>

		<guid isPermaLink="false">http://brightstartutors.com/blog/?p=237</guid>
		<description><![CDATA[Math textbooks often present formulas, even extremely important ones, without proof or justification. That&#8217;s probably fine for the student with average interest and ability, but it is often a disservice to students who really want to understand the subject. My preference would be that the books have derivations in a sidebar, with the understanding that [...]]]></description>
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		<slash:comments>1</slash:comments>
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