How Did The Greeks Know ?

How Did The Greeks Know ?

How did the Greeks know ?

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

Method of Exhaustion - Archimedes

image

                                                       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.

image

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!

image

Happy Holidays !

More Posts from T-sci-eng and Others

7 years ago
Crazy Looking Bamboo Tower Creates 25 Gallons Of Drinking Water Per Day From Thin Air
Crazy Looking Bamboo Tower Creates 25 Gallons Of Drinking Water Per Day From Thin Air
Crazy Looking Bamboo Tower Creates 25 Gallons Of Drinking Water Per Day From Thin Air
Crazy Looking Bamboo Tower Creates 25 Gallons Of Drinking Water Per Day From Thin Air
Crazy Looking Bamboo Tower Creates 25 Gallons Of Drinking Water Per Day From Thin Air
Crazy Looking Bamboo Tower Creates 25 Gallons Of Drinking Water Per Day From Thin Air

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.

7 years ago
What Have Eclipses Ever Done For Science? Quite A Lot, Actually!

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

What Have Eclipses Ever Done For Science? Quite A Lot, Actually!
What Have Eclipses Ever Done For Science? Quite A Lot, Actually!
What Have Eclipses Ever Done For Science? Quite A Lot, Actually!

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

What Have Eclipses Ever Done For Science? Quite A Lot, Actually!
What Have Eclipses Ever Done For Science? Quite A Lot, Actually!

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

What Have Eclipses Ever Done For Science? Quite A Lot, Actually!

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.

7 years ago
The Simple Physics Behind A Fidget Spinner

The simple physics behind a Fidget Spinner

When you want something to spin for a really long time you need to make sure that the friction does not slow it down.

image

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.

image

And many Fidget spinners indeed use ceramic ball bearings to keep them spinning for a long time. **

Mass Distribution

The next most crucial component is the Angular Momentum. Angular momentum is equal to the product of rotational velocity and the moment of inertia. 

image

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.

But, Why do they feel alive ?

image

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

7 years ago
In Mathematics There Is A Concept Known As ‘Conformal Mapping’ Which Allows You Convert A Given Shape
In Mathematics There Is A Concept Known As ‘Conformal Mapping’ Which Allows You Convert A Given Shape
In Mathematics There Is A Concept Known As ‘Conformal Mapping’ Which Allows You Convert A Given Shape
In Mathematics There Is A Concept Known As ‘Conformal Mapping’ Which Allows You Convert A Given Shape
In Mathematics There Is A Concept Known As ‘Conformal Mapping’ Which Allows You Convert A Given Shape

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:

image

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

7 years ago

Physical Science...In Space!

Each month, we highlight a different research topic on the International Space Station. In May, our focus is physical science.

image

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.

image

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).

image

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. 

Physical Science...In Space!

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.

image

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

7 years ago

Solar System: Things to Know This Week

10 Tools for the Armchair Astronaut, or  How to Explore the Solar System from Home

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.  

image

1. It’s Like Facebook, but for Planets

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

image

2. Keep Your Eyes on This One

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

image

3. Dateline: Deep Space

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

image

4. Space? There’s an App for That

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

image

5. A (Very) Long Distance Call

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

image

6. Collect ‘Em All

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

image

7. Ever Wanted to Drive a Mars Rover?

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

image

8. More E-Ticket Attractions

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

image

9. The Universe Is Our Classroom

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

image

10. Bring It on Home

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

Discover more lists of 10 things to know about our solar system HERE.

Follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com

7 years ago
The Magnus Effect Is Cool! Learn More About It In @veritasium Video: Https://youtu.be/2OSrvzNW9FE

The Magnus Effect is cool! Learn more about it in @veritasium video: https://youtu.be/2OSrvzNW9FE

7 years ago
But That’s Not All It Can Do. Microsoft And NASA Teamed Up To “bring” You, Yes You, To Mars.
But That’s Not All It Can Do. Microsoft And NASA Teamed Up To “bring” You, Yes You, To Mars.
But That’s Not All It Can Do. Microsoft And NASA Teamed Up To “bring” You, Yes You, To Mars.
But That’s Not All It Can Do. Microsoft And NASA Teamed Up To “bring” You, Yes You, To Mars.
But That’s Not All It Can Do. Microsoft And NASA Teamed Up To “bring” You, Yes You, To Mars.
But That’s Not All It Can Do. Microsoft And NASA Teamed Up To “bring” You, Yes You, To Mars.
But That’s Not All It Can Do. Microsoft And NASA Teamed Up To “bring” You, Yes You, To Mars.
But That’s Not All It Can Do. Microsoft And NASA Teamed Up To “bring” You, Yes You, To Mars.
But That’s Not All It Can Do. Microsoft And NASA Teamed Up To “bring” You, Yes You, To Mars.
But That’s Not All It Can Do. Microsoft And NASA Teamed Up To “bring” You, Yes You, To Mars.

But that’s not all it can do. Microsoft and NASA teamed up to “bring” you, yes you, to Mars.

Follow @the-future-now

7 years ago
Alloys: Wood’s Metal
Alloys: Wood’s Metal
Alloys: Wood’s Metal
Alloys: Wood’s Metal

Alloys: Wood’s Metal

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 )

7 years ago
Looping Thunderstorm Gifs By Mike Hollingshead
Looping Thunderstorm Gifs By Mike Hollingshead
Looping Thunderstorm Gifs By Mike Hollingshead
Looping Thunderstorm Gifs By Mike Hollingshead
Looping Thunderstorm Gifs By Mike Hollingshead

Looping thunderstorm gifs by Mike Hollingshead

  • anarcho-cawmmunism
    anarcho-cawmmunism liked this · 6 years ago
  • purebloodslytherin182
    purebloodslytherin182 liked this · 6 years ago
  • ghouls-ghouls-boos
    ghouls-ghouls-boos liked this · 6 years ago
  • replicant1955
    replicant1955 liked this · 6 years ago
  • f0rg3tm3n0t
    f0rg3tm3n0t liked this · 6 years ago
  • maeve69
    maeve69 liked this · 7 years ago
  • winnerwhinerchickendiner
    winnerwhinerchickendiner liked this · 7 years ago
  • t-sci-eng
    t-sci-eng reblogged this · 7 years ago
  • makechangenotcash
    makechangenotcash reblogged this · 7 years ago
  • titwagon
    titwagon liked this · 8 years ago
  • artasinfashion
    artasinfashion reblogged this · 8 years ago
  • panda-poes
    panda-poes reblogged this · 8 years ago
  • frostedkiwi
    frostedkiwi liked this · 8 years ago
  • the-real-satan
    the-real-satan liked this · 8 years ago
  • sonnetimo
    sonnetimo liked this · 8 years ago
  • maggie-luvs2fly
    maggie-luvs2fly liked this · 8 years ago
  • areyousureabtthat
    areyousureabtthat reblogged this · 8 years ago
  • areyousureabtthat
    areyousureabtthat liked this · 8 years ago
  • benjaminjacobfrost
    benjaminjacobfrost liked this · 8 years ago
  • bostonfly
    bostonfly reblogged this · 8 years ago
  • rawthunderhustler
    rawthunderhustler liked this · 8 years ago
  • swordlesbn
    swordlesbn liked this · 8 years ago
  • swordlesbn
    swordlesbn reblogged this · 8 years ago
  • orbitalobserver
    orbitalobserver liked this · 8 years ago
  • katemossnephew
    katemossnephew liked this · 8 years ago
  • giona-nella-balena
    giona-nella-balena liked this · 8 years ago
  • noneun
    noneun liked this · 8 years ago
  • gigiopix
    gigiopix reblogged this · 8 years ago
  • gigiopix
    gigiopix liked this · 8 years ago
  • iamslblog
    iamslblog reblogged this · 8 years ago
  • girulicchio
    girulicchio liked this · 8 years ago
  • asararug-blog
    asararug-blog liked this · 8 years ago
  • anosognosico
    anosognosico reblogged this · 8 years ago
  • daniel-1989
    daniel-1989 liked this · 8 years ago
t-sci-eng - SCIENCE AND ENGINEERING
SCIENCE AND ENGINEERING

117 posts

Explore Tumblr Blog
Search Through Tumblr Tags