Superstretchable, Supercompressible Supercapacitors

Inside - Vadim Sadovski

Curves of constant width

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The width of a circle is constant: its diameter.

But the circle is not the only shape that holds this pristine title. For instance let’s look at the Reuleaux triangle

Reuleaux triangle

A Reuleaux triangle is a shape formed from the intersection of three circular disks, each having its center on the boundary of the other two.

The Reuleaux triangle is the first of a sequence of Reuleaux polygons, curves of constant width formed from regular polygons with an odd number of sides.

Some of these curves have been used as the shapes of coins

To drill square holes.

They are not entirely square, their edges are fillets i.e the edges are rounded and not sharp.

This animation offers a good insight as to why that is so.

And in china, apparently on bicycles.

The man Guan Baihua shows his self-made multi-angle-wheel bicycle on May 6, 2009 in Qingdao of Shandong Province, China. Guan Baihua spent 18 months to complete this strange bicycle.

Other shapes of constant width

There are other shapes of constant width beside the Reuleaux triangle ( that has been discussed in this post ), a whole bunch of them really. Do take a look at them. ( links below )

I will leave you guys with my favorite one.

More:

If this post fascinated you, i strongly suggest you check these out. They go in-depth with the mathematics that underlies these curves and talk about other cool stuff:

An animation of non-circular rollers

Shapes and Solids of Constant Width - Numberphile  

Shapes of constant width

Reuleaux Polygons,           

Edit:

For those who are wondering if these are something that one would stumble upon on a regular basis. You may not find perfect ones but similiar ones definitely.

I found mine on a really old BMI calculator thingy. ( not sure what you would call it )

Have fun exploring !

How platinum powers the world

Platinum bars. Image: Sprott Money@Flickr 

Platinum is one of the most valuable metals in the world. Precious and pretty, it’s probably best known for jewelry – and that is almost certainly its oldest use. But its value has become far greater than its decorative ability; today, platinum powers the world. From agriculture to the oil markets, energy to healthcare, we use platinum far more than we realise.

1. Keep the car running

Platinum is needed to make fuel for transport. Image: Pixabay

Platinum catalysts are crucial in the process that converts naphtha into petrol, diesel, and jet-engine fuel, which are all vital to the global economy. The emissions from those petroleum fuels, however, can be toxic, and platinum is also crucial in the worldwide push to reduce them through automotive catalytic converters. In fact, 2% of global platinum use in 2016 was in converting petroleum and 41% went into reducing emissions – a circle of platinum use that’s more impressive than a ring.

2. Feed the world

Nitric acid is a by-product of platinum which is used in fertilisers. Image: Pixabay

Another vital global sector that makes use of platinum catalysts is agriculture. Without synthetic fertilisers, we would not be able to produce nearly as much food as we need. Nitric acid is essential for producing those fertilisers and platinum is essential for producing nitric acid. Since 90% of the gauzes required for nitric acid are platinum, we may need to use more of it as we try to meet the global food challenge.

3. Good for your health

A pacemaker. Image: Steven Fruitsmaak@Wikimedia Commons 

Platinum is extremely hard wearing, non-corrosive, and highly biocompatible, making it an excellent material to protect medical implants from acid corrosion in the human body. It is commonly used in pacemakers and stents. It is also used in chemotherapy, where platinum-based chemotherapeutic agents are used to treat up to 50% of cancer patients.

Keep reading

What can we learn from ants and plants?  

That’s what IBMer Mauro Martino set out to answer in his award-winning data visualization, Network Earth. It explores nature’s interconnected relationships, and how they affect each other and our planet. By making the complex but important topics easier to visualize, we hope to help make more of them accessible to all.

It’s #MoleDay! Here’s an up-to-date version of my mole explainer: https://ift.tt/2D1ucqz https://ift.tt/2N8Vcaf

On the cross product

Understand the concept and not the definition.

If you have studied vectors, then the notion of a cross product is something that you might be familiar with.

Although it is taught in many colleges and schools in its mathematical glory, this post aims to supplement the same but with an real-life example.

The cross product

The magnitude of the cross product is the area of the parallelogram with two sides A and B.

The orientation of the cross product is orthogonal to the plane containing this parallelogram. 

Why on earth is it orthogonal ? Like seriously…

I mean this is one of the burning questions regarding the cross product and yet for some reason, textbooks don’t get to the bottom of this.

It is modeling a real life scenario!!

The scenario being :

When you try to twist a screw inside a block in the clockwise direction like so, the nail moves down and vice versa.

i.e When you move from the screw from u to v, then the direction of the cross product denotes the direction the screw will move.

That’s why the direction of the cross product is orthogonal. It’s really that simple :D

Have a good day!

A2A : Anonymous

Coloring Book Celebrates Mathematical Beauty of Nature with Hand-Drawn Golden Ratio Illustrations

Human fingers can detect nano-size objects. This means you not only have the ability to feel a tiny bump the size of a large molecule, but if your finger was the size of Earth, you could determine the difference between a house and a car. Source

Adieu 2016 - Best of FYP!

2016 has been a great year for FYP!

And we would like to conclude it with some of the best posts that we have been able to produce

1. Black hole are not so black - series

Part - I , II, III

2.‘Katana’ - A sword that can slice a bullet

3. A denied stardom status - Jupiter

4. The Pythagoras Cup

5. On Pirates and Astronomers                                                           

6. Behold- The Space Shuttle Tile

7. Principle of Least Effort

8. Leidenfrost Effect

9. Major Types of Engines

10. A holy matrimony of Pascals and Sierpinski’s Triangle

11. Curves of constant width

12. Smooth Ride, Bumpy Road

Thank you so much following us ! Have a great weekend :D

 - Fuck Yeah Physics!

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