Curiosities for Artists and Engineers

Goldbach's Conjecture "The longest-standing math problem is  Goldbach's Conjecture,  posed by the Russian mathematician in 1742, according to the Guinness Book of World Records. The theorem states that every even positive integer greater than three is the sum of two prime numbers." --  Zoe Mintz - IBTimes I was interested to get a feel for this conjecture, where an even number was the sum of two prime numbers. I took a list of the prime numbers up to 32767, and knew I'd have enough prime numbers to cover to 32768. First, I looked to see if these numbers matched the condition. Using Java, a quickly found that these first few even numbers (the first 16000) matched at least one pair of prime numbers. Next I wanted to see how constrained these values were. Instead of checking whether two primes existed that added up to N, I checked how many unique pairs of primes matched. Matching more than one pair was a dramatic understatement. By 3000, each even integer cou...

Ring Approach Around Atmospheric Issues There are upsides and downsides to the earth's atmosphere. The greatest advantage is that it provides the oxygen needed for life, our life.  It provides a medium to navigate through using aerodynamic flight.  The atmosphere generally provides humidity that can condense into rainwater and drinking water for consumption and irrigation. From an engineering standpoint, it has numerous disadvantages: Puncturing the atmosphere costs fuel through drag. Weather systems in the atmosphere interfere with operation. Solar energy collection is less efficient due to the light-scattering factors of the atmosphere. The Ring The ring around the Earth is a self-supporting scaffolding and arch that circumscribes the Earth. Located at around 40,000 to 60,000 feet in the atmosphere, it would be accessible by winged aircraft which could land on the ring, and then dock in a pressurized terminal. Living chambers in the ring could be pressuri...

43 American Cities for Nerdy, Trivial Mathematicians 43 Special American Cities for the Trivial Math Nerd. I like this chart because it combines a few services that are available on the Internet and shows the flexibility of a Mash-Up.  Alledonia, Ohio  43902 Arbovale, West Virginia  24915 Ashley, North Dakota  58413 Burnips, Michigan  49314 Canova, South Dakota  57321 Coaldale, Colorado  81222 Cross Timbers, Missouri  65634 Cuney, Texas  75759 Cynthiana, Ohio  45624 Dora, Missouri  65637 East Wenatchee, Washington  98802 Glenmora, Louisiana  71433 Great Falls, Montana  59403 House Springs, Missouri  63051 Humble, Texas  77346 Kansas City, Kansas  66105 Kensal, North Dakota  58455 Las Vegas, Nevada  89145 Lawrence, Mississippi  39336 Madison, Alabama  35757 Mandan, North Dakota  58554 Mcbrides, Michigan  48852 Miam...

Here in the United States, dates are commonly written in a month-slash-day format. April 7th would be written as 4/7 with April, the forth month, followed by a divided-by sign, then 7, for the seventh day.  As you look at the date, it can also be viewed as a fraction, 4/7th. I wondered if there were any days where the representation of the day, month-slash-day, would correspond to the portion of the year that had passed. I hadn't run across anyone who had looked into that before. Ultimately, I coded some Excel formulas and found the days and found that 8/13, August 13, contained the moment which was 8/13ths of the way through a non-leap year. 8/13 But before I did that, I thought through some scenarios: Improper Fractions If the answer turned out to be 6/10 or 3/9, I would not consider that a good answer because something special like a day that represents the fraction of the year that has passed can't be "well, if you arrange it as an improper fraction, ......