Greeks had a strong geometric approach towards problems and as a result their methods are very intuitive.
In this post, we will look at the Method of exhaustion formulated by Archimedes that stands out as a milestone in the history of mathematics
Source
In order to find the bounds of pi, Archimedes came up with a remarkably elegant ‘algorithm’, which is as follows:
Lower bound
Inscribe a n-sided polygon in a circle —> Measure its perimeter(p) —> Measure its diameter(d) —> pi_min = p/d —-> Repeat with n+1 sides.
Upper bound
Circumscribe a n-sided polygon in a circle —> Measure its perimeter(p) —> Measure its diameter(d) —> pi_max = p/d —-> Repeat with n+1 sides.
And by following this procedure one could obtain the upper and lower bounds of pi !
Heres an animation made on geogebra for a circle of diameter 1. Watch how the lower and upper bounds vary.
Archimedes did this for a 96 sided polygon and found the value of pi to be between 3.14103 and 3.1427. This is a good enough approximation for most of the calculations that we do even today!
Happy Holidays !
Crazy Looking Bamboo Tower Creates 25 Gallons of Drinking Water Per Day From Thin air
This crazy looking tower creates 25 gallons of drinking water per day from thin air. It’s basically an atmospheric water collector which gathers dew from the air.
“…The 9 m tall bamboo framework has a special fabric hanging inside capable to collect potable water from the air by condensation…”
It’s called the WarkaWater:
“…The name ‘WarkaWater’ comes from the Warka Tree, a giant wild fig tree native to Ethiopia, traditionally used for public gatherings and school education. The Warka Tree is an archetype of the Biennale theme ‘Common Ground’…”
The simple and practical, yet elegant design powers out ahead of any of the commercial atmospheric water generators on the market which cost thousands more to build than this.
This is a wonderful water generation idea, that’s inexpensive, and actually beautiful to look at.
Water is life, and being designed after a tree. This is a real Tree of Life.
What have eclipses ever done for science? Quite a lot, actually!
The first measurement of the width of the Atlantic ocean in the 16th Century
When British settlers arrived in Virginia in the US, they weren’t sure how far across the globe they’d gone. They recorded the local time of a total eclipse of the moon - which is seen all across the night-time side of the planet. Their colleagues in London did the same, and when the travellers returned they could figure out the five hour time difference.
Edmond Halley discovered that the moon is moving away from the Earth
Halley realised you could back-calculate when previous eclipses would have occurred. But he noticed a mismatch between his predictions and the history books. The reason, he discovered, what that he was assuming the moon stayed the same distance from the Earth. It is actually getting further at about the rate your fingernails grow. And that means that one day (in a few million years, that is), the moon will be too far away to create any more total solar eclipses.
In 1919 a solar eclipse proved Einstein’s theory of relativity
Einstein’s theory predicted that the sun’s gravity should bend the light of nearby stars, meaning that in theory we should be able to see stars that are hidden just behind the sun. However, sunlight always blocks our view of these stars, and it was only during a solar eclipse that there was a short window to see if hidden stars were visible, as predicted. Astronomer Arthur Eddington travelled to West Africa and took photos that proved Einstein right.
Scientists still use solar eclipses today
It’s very hard to study the sun’s corona - a tenuous hot gas, which just one millionth of the light intensity of the sun. The shapes and lines of the corona show the nature of the sun’s magnetic field, and are only visible to study during an eclipse. NASA are also using this opportunity to help create the first thermal map of Mercury!
Want to know more? Watch our full video.
When you want something to spin for a really long time you need to make sure that the friction does not slow it down.
And we can do this by adopting ball bearings. This is so because friction offered due to rolling is much smaller than due to sliding.
And many Fidget spinners indeed use ceramic ball bearings to keep them spinning for a long time. **
The next most crucial component is the Angular Momentum. Angular momentum is equal to the product of rotational velocity and the moment of inertia.
And by distributing more mass towards the edge, the fidget spinner gains high moment of inertia keeping it spinning longer.
That’s why the spinners have that weird peculiar shape.
The angular momentum of a fidget spinner happens to point outwards from the spinner’s center.
And so to change the direction of the momentum — rotating the spinner with your fingers — you must apply a force. You push on the spinner, and the spinner pushes back on you.
That’s why a fidget spinner feels like it fights you, like it’s alive.
- Nerdist
A very fascinating toy nevertheless!
** Spin Test : Ceramic Vs Steel ball bearings
*** Fidget spinner trick shots
In mathematics there is a concept known as ‘Conformal Mapping’ which allows you convert a given shape to a completely different one by making a transformation.
In the joukowski transform you take all the points on a circle and apply the following transform:
And the resulting transformed points resemble an aerofoil shape. Pretty cool huh ?
** Conformal mappings are a really cool topic in complex analysis but also equally extensive. If you want to know more about them click here
Each month, we highlight a different research topic on the International Space Station. In May, our focus is physical science.
The space station is a laboratory unlike any on Earth; on-board, we can control gravity as a variable and even remove it entirely from the equation. Removing gravity reveals fundamental aspects of physics hidden by force-dependent phenomena such as buoyancy-driven convection and sedimentation.
Gravity often masks or distorts subtle forces such as surface tension and diffusion; on space station, these forces have been harnessed for a wide variety of physical science applications (combustion, fluids, colloids, surface wetting, boiling, convection, materials processing, etc).
Other examples of observations in space include boiling in which bubbles do not rise, colloidal systems containing crystalline structures unlike any seen on Earth and spherical flames burning around fuel droplets. Also observed was a uniform dispersion of tin particles in a liquid melt, instead of rising to the top as would happen in Earth’s gravity.
So what? By understanding the fundamentals of combustion and surface tension, we may make more efficient combustion engines; better portable medical diagnostics; stronger, lighter alloys; medicines with longer shelf-life, and buildings that are more resistant to earthquakes.
Findings from physical science research on station may improve the understanding of material properties. This information could potentially revolutionize development of new and improved products for use in everything from automobiles to airplanes to spacecraft.
For more information on space station research, follow @ISS_Research on Twitter!
Make sure to follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com
At this very moment, spacecraft are surveying the solar system, from Mars, to Saturn, to Pluto and beyond. Now you can ride along to see the latest discoveries from deep space. For this week’s edition of 10 Things, we’ve assembled a toolkit of 10 essential resources for the desktop astronaut.
Or is it more of a Hitchhiker’s Guide to the Solar System? Whatever one calls it, our planets page offers quick rundowns, as well as in-depth guides, for all the major bodies in the solar system. Explore from the sun all the way to the Oort Cloud.
+ Peruse the planets + See how objects in the solar system stack up against each other
If you still haven’t tried Eyes on the Solar System, you’re missing out. This free, downloadable simulation app lets you tour the planets and track the past, current and future positions of spacecraft–all in 3D. Eyes on the Solar System uses real NASA data to help you take a virtual flight across both space and time.
+ Prepare for departure
With so much exploration underway, discoveries and new insights into the solar system come at a pace that borders on bewildering. NASA is rewriting the textbooks, literally, on a regular basis. Relax, though: there are several easy ways to stay up to date with what’s happening in space.
+ See the latest headlines + Stay connected on social media: Twitter, Facebook, Instagram + Find more top NASA social media accounts
NASA offers phone and tablet apps for star gazing, pictures, news, 3D tours, satellite tracking, live NASA TV and many other kinds of info.
+ Start downloading + See other cool apps
We’re in constant communication with spacecraft all over the solar system. The Deep Space Network is a global network of giant antenna dishes that makes it possible. With this online app, you can learn how it works – and even see which spacecraft are phoning home right now.
+ Deep Space Network (DSN) Now
Spacecraft 3D is an augmented reality (AR) application that lets you learn about and interact with a variety of spacecraft that are used to explore our solar system, study Earth and observe the universe. Print out the AR target and your camera will do the rest, making the spacecraft appear in 3D right in front of you. Learn more about these robotic explorers as they pop up on your desk, in your hand, or on your dog’s head.
+ Download Spacecraft 3D + See more cool 3-D resources from NASA
This site will give you a 3D look at the Mars Curiosity rover, along with some of the terrain it has explored. It will even let you take the controls.
+ Experience Curiosity
But wait, there’s more. NASA offers a variety of other fascinating (and free) online experiences, all based on actual data from real missions. Here are a few to explore:
+ Mars Trek + Vesta Trek + Moon Trek
Studying the solar system makes for a compelling route into learning and teaching science, engineering and math. We have some great places to start.
+ Find resources for teachers + Build your own solar system with your classroom
After you’ve toured the far reaches of the solar system, you can always come home again. When you have spent time studying the harsh conditions on our neighboring planets, the charms of a unique paradise come into sharp focus, the place we call Earth.
+ Watch a real-time video feed from Earth orbit + See a daily global view of our planet from a million miles away + Hold the earth in your hands with the Earth Now mobile app
Follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com
The Magnus Effect is cool! Learn more about it in @veritasium video: https://youtu.be/2OSrvzNW9FE
But that’s not all it can do. Microsoft and NASA teamed up to “bring” you, yes you, to Mars.
Follow @the-future-now
Also known as Lipowtiz’s alloy as well as the commercial names of Cerrobend, Bendalloy, Pewtalloy, and MCP 158 among others, Wood’s metal is a bismuth alloy consisting of 50% bismuth, 26.67% lead, 13.33% tin, and 10% cadmium by weight. Named for the man who invented it, a Barnabas Wood, Wood’s metal was discovered/created by him in 1860.
Wood’s metal is both a eutectic and a fusible alloy, with a low melting temperature of approximately 70 °C (158 °F). While none of its individual components have a melting temperature of less than 200 °C, a eutectic alloy can be considered as a pure (homogeneous) substance and always has a sharp melting point. If the elements in a eutectic compound or alloy are not as tightly bound as they would be in the pure elements, this leads to a lower melting point. (Eutectic substances can have higher melting points, if its components bind tightly to themselves.)
Useful as a low-temperature solder or casting metal, Wood’s metal is also used as valves in fire sprinkler systems. Thanks to its low melting temperature, Wood’s metal melts in the case of a fire and thanks to the bismuth it is made from, the alloy also shrinks when it melts (bismuth, like water ice, is one of the few substances to do so) which is the key to setting off the sprinkler system. Wood’s metal is also often used as a filler when bending thin walled metal tubes: the filler prevents the tube from collapsing, then can be easily removed by heating and melting the Wood’s metal. Other applications include treating antiques, as a heat transfer medium in hot baths, and in making custom shaped apertures and blocks for medical radiation treatment.
With the addition of both lead and cadmium, however, Wood’s metal is considered to be a toxic alloy. Contact with bare skin is thought to be harmful, especially once the alloy has melted, and vapors from cadmium containing alloys are also quite dangerous and can result in cadmium poisoning. A non-toxic alternative to Wood’s metal is Field’s metal, composed of bismuth, tin, and indium.
Sources: ( 1 - image 4 ) ( 2 - image 2 ) ( 3 ) ( 4 )
Image sources: ( 1 ) ( 3 )
Looping thunderstorm gifs by Mike Hollingshead