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	<title>blog.brightstartutors.com &#187; Thrilling Math</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>
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		<slash:comments>1</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>
		<wfw:commentRss>http://brightstartutors.com/blog/2010/01/14/newton-verifies-the-law-of-gravity/feed/</wfw:commentRss>
		<slash:comments>1</slash:comments>
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		<title>The Wonders of WolframAlpha</title>
		<link>http://brightstartutors.com/blog/2010/01/08/the-wonders-of-wolframalpha/</link>
		<comments>http://brightstartutors.com/blog/2010/01/08/the-wonders-of-wolframalpha/#comments</comments>
		<pubDate>Fri, 08 Jan 2010 07:27:58 +0000</pubDate>
		<dc:creator>curiousCharacter</dc:creator>
				<category><![CDATA[Computers and Mathematics]]></category>
		<category><![CDATA[Learning Math]]></category>
		<category><![CDATA[Thrilling Math]]></category>
		<category><![CDATA[Trig/PreCalculus]]></category>

		<guid isPermaLink="false">http://brightstartutors.com/blog/?p=388</guid>
		<description><![CDATA[It is unworthy of excellent men to lose hours like slaves in the labor of calculation.
Gottfried Wilhelm Leibniz

I have often told students that becoming good at math is a lot like becoming good at a sport or at playing an instrument – practice is extremely  important. Hours and hours of practice.

However, there is a [...]]]></description>
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		<slash:comments>6</slash:comments>
		</item>
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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>
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		<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>
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		<title>The Mathematics of Monsters</title>
		<link>http://brightstartutors.com/blog/2009/10/01/the-mathematics-of-monsters/</link>
		<comments>http://brightstartutors.com/blog/2009/10/01/the-mathematics-of-monsters/#comments</comments>
		<pubDate>Fri, 02 Oct 2009 03:21:49 +0000</pubDate>
		<dc:creator>curiousCharacter</dc:creator>
				<category><![CDATA[Thrilling Math]]></category>

		<guid isPermaLink="false">http://brightstartutors.com/blog/?p=334</guid>
		<description><![CDATA[








Here is the familiar image of King Kong atop the Empire State Building. There&#8217;s something profoundly incorrect in how he is depicted, a problem that is shared with almost all giant creatures in the movies, be they flies, dragons, or humans. The problem involves some math, which is why I&#8217;m discussing it here.




Before I can [...]]]></description>
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		<slash:comments>0</slash:comments>
		</item>
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		<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>
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		<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>
		</item>
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		<title>Galileo Measures the Mountains of the Moon</title>
		<link>http://brightstartutors.com/blog/2009/05/28/galileo-measures-the-mountains-of-the-moon/</link>
		<comments>http://brightstartutors.com/blog/2009/05/28/galileo-measures-the-mountains-of-the-moon/#comments</comments>
		<pubDate>Thu, 28 May 2009 10:41:19 +0000</pubDate>
		<dc:creator>curiousCharacter</dc:creator>
				<category><![CDATA[Thrilling Math]]></category>
		<category><![CDATA[Math]]></category>

		<guid isPermaLink="false">http://brightstartutors.com/blog/?p=214</guid>
		<description><![CDATA[







Four hundred years ago, in 1609, Galileo heard about the newly invented telescope. He succeeded in making one for himself, and he immediately used it to look at the night sky. The things he discovered were astonishing: moons around Jupiter, the phases of Venus, and the stars of the Milky Way.





When he examined the moon, [...]]]></description>
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		<slash:comments>0</slash:comments>
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