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Pictured is a Delta IV rocket launch from Cape Canaveral on November 21st, 2010. The image is a 20 second exposure taken at dusk, shot from about 100 miles west of the launch site. The launch placed a classified payload in orbit for the United States Air Force.
Difficult but not impossible to catch against the dawn or dusk sky, spotting an extreme crescent moon can be a challenge. The slender crescent pictured was shot 30 minutes before sunrise when the Moon was less than 20 hours away from New.� A true feat of visual athletics to catch, a good pair of binoculars or a well aimed wide field telescopic view can help with the hunt.
The Sun is our nearest star, and goes through an 11-year cycle of activity. This image was taken via a properly filtered telescope, and shows the Sun as it appeared during its last maximum peak in 2003. This was during solar cycle #23, a period during which the Sun hurled several large flares Earthward. The next solar cycle is due to peak around 2013-14.
Located in the belt of the constellation Orion, Messier 42, also known as the Orion Nebula is one of the finest deep sky objects in the northern hemisphere sky. Just visible as a faint smudge to the naked eye on a clear dark night, the Orion Nebula is a sure star party favorite, as it shows tendrils of gas contrasted with bright stars. M42 is a large stellar nursery, a star forming region about 1,000 light years distant.
Orbiting the planet in Low Earth Orbit (LEO) every 90 minutes, many people fail to realize that you can see the International Space Station (ISS) from most of the planet on a near-weekly basis. In fact, the ISS has been known to make up to four visible passes over the same location in one night. The image pictured is from the Fourth of July, 2011 and is a 20 second exposure of a bright ISS pass.
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Next to the Sun, the two brightest objects in the sky are the Moon and the planet Venus. In fact, when Venus is favorably placed next to the Moon, it might just be possible to spot the two in the daytime. Another intriguing effect known as earthshine or ashen light is also seen in the image on the night side of the Moon; this is caused by sunlight reflected back off of the Earth towards our only satellite.
A mosaic of three images taken during the total lunar eclipse of December 21st, 2010. The eclipse occurred the same day as the winter solstice. The curve and size of the Earth�s shadow is apparent in the image.
Mathematical Curiosities by Alfred S. Posamentier and Ingmar Lehmann
On sale now.
Today, we�ll delve into the exciting and exhilarating world of mathematics. Wait, wait, come back�
This week we�ll be looking at Mathematical Curiosities: A Treasure Trove of Unexpected Entertainments out from Prometheus Books by Alfred S. Posamentier and Ingmar Lehmann.
Fans of this space will also remember our reviews of The Glorious Golden Ratio, The Secrets of Triangles and Magnificent Mistakes also by Lehmann and Posamentier.
Mathematical Curiosities aptly demonstrates that math doesn�t have to journey into its higher dimensions to be bizarre. The authors start with some great examples straight out of elementary school math class and assume no prior knowledge of algebra and higher mathematics. There�s lots to delve into here, and the authors take the reader on an exciting (yes, math can be exciting!) journey through alternate counting systems, mathematical curiosities and peculiarities, and much more.
Some of our faves:
-����� Did you know that you can (sometimes) arrive at the right answer� using the wrong method? These �howlers� come straight out of math class, one of which is depicted in Bogdanov-Belski�s 1895 painting entitled �A Difficult Assignment.�
-����� The number eight is the only cube number smaller than a square number by one. The Chinese consider this to be a �lucky� number for this reason. Further wackiness ensues with much larger numbers along the decimal scale, and one must remember that in some cases, it took centuries to prove that such things were true through an infinite series of numbers.
-����� The reverse of the prime number 193,939 � 939,391 � is also prime. Four other variations of the same number � 919,393, 391,939, 939,193 and 393,919 are also prime. Then there�s the world of mersene primes, perfect numbers and much more�
And speaking of alternate counting systems, some of the ancient systems of mathematics, such as the Babylonian system of long division and multiplication are also addressed in the book.
Some mysteries are recently solved or remain open, and examples abound in everyday life. One great example addressed in the book is Kepler�s Conjecture, only recently solved in 1998. Kepler�s Conjecture addresses the most efficient use of space when stacking spherical objects, be it oranges or cannon balls. A seemingly straight forward dilemma, problems such as these can prove to be devilishly difficult!
The last half of the book is dedicated to a rapid fire selection of mathematical teasers that would make a great addition to a classroom test for extra credit.
Three math examples from the book;
-What are the probabilities that particular calendars dates land on the same day of the week? Anyone who follows our musings about various world calendars, Friday the 13ths and other vagaries of astronomical timekeeping knows how wacky this can be.
-Where on Earth can you walk one mile south, one mile west and one mile north and end up back where you began?
-What�s the smallest number with exactly 28 divisors?
And yes, solutions are provided, just in case some of these keep you awake at night� yeah, it happened to us too!
Be sure to give Mathematical Curiosities a read for some rip-roaring good puzzles!
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