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Martin Roberts
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Martin Roberts

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Fun facts for your next dinner party.
I have compiled a list of 10 most interesting yet fascinating science facts that I have come across in the recent past days.
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interesting read.
Scientists think they might be able to explain why we need men to effectively reproduce. 
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now this is what i call a flat screen tv!
Forget buying a clunky wall mount for your TV... what if you could stick it up like a fridge magnet? LG Display is hoping you'll do just that. The compan
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Really interesting idea...
Farms dotted with the gigantic spinning blades of wind turbines have become a standard sight on long-distance road trips, but what if there was another way to capture energy from the wind? A...
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All these decades of similar "What's next in the sequence?", I have never seen this interesting one.
Richard Green originally shared to Mathematics:
 
A Curious Property of 82000

The number 82000 in base 10 is equal to 10100000001010000 in base 2, 11011111001 in base 3, 110001100 in base 4, and 10111000 in base 5. It is the smallest integer bigger than 1 whose expressions in bases 2, 3, 4, and 5 all consist entirely of zeros and ones.

What is remarkable about this property is how much the situation changes if we alter the question slightly. The smallest number bigger than 1 whose base 2, 3, and 4 representations consist of zeros and ones is 4. If we ask the same question for bases up to 3, the answer is 3, and for bases up to 2, the answer is 2. The question does not make sense for base 1, which is what leads to the sequence in the picture: [undefined], 2, 3, 4, 82000.

The graphic comes from a blog post by Thomas Oléron Evans. Most of the post discusses the intriguing problem of finding the next term in this sequence, and whether the next term even exists. In other words, does there exist an integer greater than 1 whose representations in bases 2, 3, 4, 5, and 6 all consist entirely of zeros and ones? 

The number 82000 does not satisfy these conditions, because the representation of this number in base 6 is 1431344. This means that the next number in the sequence, if it exists, must be some number bigger than 82000 whose representations in bases 2, 3, 4, and 5 all consist entirely of zeros and ones. Unfortunately, even these weaker conditions are very difficult to satisfy. An exhaustive search has been carried out up to 3125 digits in base 5 and no solution exists in this range. 

The upshot of this is that, if the next term in the sequence exists, it must have more than 2184 digits in base 10. (The 2184 comes from multiplying 3125 by the base 10 logarithm of 5.) However, there is also no known proof that the next term in the sequence does not exist.

Relevant links

Thomas Oléron Evans's blog post has much more discussion of this problem, at http://www.mathistopheles.co.uk/maths/covering-all-the-bases/solution-covering-all-the-bases/

Details of the exhaustive search can be found in the notes to the sequence http://oeis.org/A146025 in the On-Line Encyclopedia of Integer Sequences.

There is a nice online number base converter tool at http://www.cleavebooks.co.uk/scol/calnumba.htm

#mathematics #sciencesunday  
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a great experiment for the inquisitive. Always a great object lesson for students to first try to guess what will happen before they see the answer.
Paul Spoerry originally shared to Caturday:
 
What Happens When You Drop A Magnet Through A Copper Tube?
The magnet induced a current in the copper pipe, which in turn produced a magnetic field. The direction of this current then opposed the change in the magnet’s field, resulting in the magnet being repelled and thus falling more slowly. Neat. 

src: http://goo.gl/oME6U4 #ScienceIsAwesome   #Science   #ScienceSunday  
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Interesting video on how poverty can change your brain.
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Have him in circles
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Martin Roberts

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Necessity is the mother of all innovation!
The heat is stifling, the soil dry as a bone, and a new law in drought-stricken California restricts sprinklers. It is a kind of make-over which is becoming increasingly common among home-owners in California, which is now in the fourth year of a historic drought. Paula Pearson, who lives in Escondido, just north of San Diego, is one of those who has turned off her sprinkler faucet.
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this matches my experiences in the tech community. What about yours?
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this is amazing! I want one.
 
Robot Master Chef Cooks 2,000 Recipes, Cleans Up, Does the Dishes

Would you buy it?

More at: http://www.industrytap.com/robot-master-chef-cooks-2000-recipes-cleans-dishes/28765
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Just awesome!
I have always loved how something as simple as a pentagon can lead to such non-trivial mathematical connections such as the golden ratio.
 
The formula for the area of the regular #pentagon .
A basic intermediate step provides the radius for both the inscribed and circumscribed #circle , which are in themselves interesting.
Where index n is used, the equations are valid for any regular polygon. For the pentagon in particular, we take another step to find that the d/s ratio is the golden ratio. #goldenratio  
For other regular polygons, this ratio can be calculated with 2*cos(π/n), leading to the same results that are found with just #trigonometry , which is shown between these two steps.
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interesting idea.
One of Lifehacker's main tasks is to help you save money. But once you've saved money, where should you spend it in order to maximize the usefulness of your money spent—or even your happiness? To answer that, just look at what you spend your day doing, proportionally, and allocate money accordingly. I'm going to call it the comfort principle.
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math, science and tech geek, iOS developer, teacher - husband & very proud dad.
Introduction
Hi everyone. My name is Martin Roberts, and I am a geek. I spend my days and nights doing math, computing and data analysis. I learn about funky machine learning algorithms that will soon revolutionize the world. I make educational apps for kids. I teach math. And I am a very proud husband and Dad.

Having completed my PhD in nuclear physics, I spent some time doing computational physics in medical research, and then worked for a web startup company at the height of the web 2.0 craze. Combining these interests with my professional training as a high school math teacher, I later joined the millions of others and developed some educational and math apps for the iPhone and iPad.

I spend my days as an Assistant Director at Australia's National Statistical Agency managing the dissimenination of their statistical collections, and in true ninja style, by night I hack away as an covert Data Scientist attempting to devise new and improved statistical machine learning algorithms for snazzy stuff applications like Automated Essay Scoring.

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