Pi Day and Other Interesting Numbers: Significance and Applications in Mathematics and Science

March 14, 2023 / esfein / Leave a comment

https://commons.wikimedia.org/wiki/File:Matheon2.jpg

March 14th is known as Pi Day, a day that celebrates the mathematical constant π (pi), which is approximately 3.14. Pi Day has become an annual event that celebrates not only pi but also other interesting numbers that have significance in mathematics and science. This paper explores the history and significance of Pi Day and other interesting numbers that have captured the imagination of mathematicians and scientists around the world.

Pi Day

Pi Day is celebrated on March 14th, as the first three digits of pi are 3.14. The day was first celebrated in 1988 by physicist Larry Shaw at the Exploratorium in San Francisco. Since then, Pi Day has become an annual event celebrated by math enthusiasts around the world [1]. On Pi Day, people celebrate by reciting the digits of pi, holding pie-eating contests, and engaging in other math-related activities.

Significance of pi

Pi is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is an irrational number, meaning that it cannot be expressed as a finite decimal or fraction. Pi is an essential concept in mathematics and has numerous applications in physics, engineering, and other sciences [2]. The discovery and calculation of pi have been a significant milestone in the development of mathematics throughout history.

Other interesting numbers

https://commons.wikimedia.org/wiki/
File:Golden_ratio_segments.png

Pi is not the only number that has captured the imagination of mathematicians and scientists. Here are some other interesting numbers:

e: Euler’s number, also known as the natural logarithm, is a mathematical constant that is approximately equal to 2.718. It is used in calculus, probability, and other fields of mathematics and science [3].
Golden ratio: The golden ratio is a mathematical concept that describes the ratio of two quantities in which the ratio of the larger quantity to the smaller quantity is the same as the ratio of the sum of the quantities to the larger quantity. It is approximately equal to 1.618 and is often found in nature, art, and architecture [4].
Avogadro’s number: Avogadro’s number is a constant that represents the number of particles (atoms or molecules) in one mole of a substance. It is approximately equal to 6.022 x 10^23 and is used in chemistry and physics [5].
The Fibonacci sequence: The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding numbers. The sequence starts with 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on. The Fibonacci sequence appears in various natural phenomena, such as the arrangement of leaves on a stem and the growth patterns of seashells [6].

Conclusion

In conclusion, Pi Day and other interesting numbers have significant meaning and applications in mathematics and science. Pi is an essential concept that represents the ratio of a circle’s circumference to its diameter and has numerous applications in various fields. Other interesting numbers, such as e, the golden ratio, Avogadro’s number, and the Fibonacci sequence, have also played critical roles in the development of mathematics and science.

Source List:

“Celebrating Pi Day,” Exploratorium, accessed March 14, 2023, https://www.exploratorium.edu/pi
“Pi,” Wolfram MathWorld, accessed March 14, 2023, https://mathworld.wolfram.com/Pi.html
“e,” Wolfram MathWorld, accessed March 14, 2023, https://mathworld.wolfram.com/e.html
“The Golden Ratio,” Wolfram MathWorld, accessed March 14, 2023, https://mathworld.wolfram.com/GoldenRatio.html
“Avogadro’s Number,” Encyclopedia Britannica, accessed March 14, 2023, https://www.britannica.com/science/Avogadros-number
“Fibonacci Numbers and Nature,” The Fibonacci Association, accessed March 14, 2023, https://www.fibonacciassociation.org/Fibonacci-number-in-nature.html

Computer Chips Modeled After the Human Brain

September 2, 2013 / esfein / 1 Comment

I dare you to look at contemporary computer chips and not admire their abilities.　 The most impressive example may be the realized dream of hand-sized smart-phones, pieces of technology we already tend to take for granted. And yet – with all their condensed might packed into a few square centimetres, those chips are nearing their developmental boundaries.

Try to open your computer case and have a look. Ignore the dust! See all those messy cables inside? Modern computer architecture is crippled by the fact that data has to flow between the different parts of the computer: The CPU (central processing unit), hard-drive, the RAM, the video card, etc. (namely – those green cards that you see inside the computer case). Although tremendous efforts have been made to accelerate those transitions, the data flow between those parts still poses a serious bottleneck on the performance of computers since software commands have to be executed sequentially.

Related Article: Electronic Brain Implants Increase Intelligence

A new study from Boise State University suggests a better solution to the problem: computer chip architecture modeled after the human brain. Instead of a central processing unit overwhelmed by data flow from different computer parts, the new architecture will be based on the way the human brain functions. Multiple areas – each one processing it’s own part, contribute together to create the bigger picture. This kind of architecture eliminates the need for the major processing and memory units. Instead of a hard-drive, the RAM, the video-card and most probably the CPU itself, a new kind of universal electronic chip will process and store the data on its own.

According to the principal investigator of the research grant, Elisa Barney Smith,

By mimicking the brain’s billions of interconnections and pattern recognition capabilities, we may ultimately introduce a new paradigm in speed and power, and potentially enable systems that include the ability to learn, adapt and respond to their environment.

The neural approach is now becoming practical thanks to the on-going development of a new type of resistor: the memristor. Memristors can be tweaked to new resistance levels by applying and removing electric currents. Memristors “remember” the last resistance applied to them even after the power is removed. In simple words – a storage effect appears. An idea first conceived in 1971, for many years memristors puzzled physicist and engineers as a theoretical missing link component until recent developments finally made them practical. Although not yet commercially used, memristors are already taking active parts in research.

Dexter Johnson from The Nanoclast goes into greater detail regarding memristors:

The memristor has been on a rapid development track ever since and has been promised to be commercially available as early as 2014, enabling 10 times greater embedded memory for mobile devices than currently available.

The obsolescence of flash memory at the hands of the latest nanotechnology has been predicted for longer than the commercial introduction of the memristor. But just at the moment it appears it’s going to reach its limits in storage capacity along comes a new way to push its capabilities to new heights, sometimes thanks to a nanomaterial like graphene.

Using memristors, the team hopes to apply algorithms inspired by the interaction between the neural synapses of the human brain. The effect should follow the intricate patterns our brain implements to process and store data.

Related Article: Of Cyborg Monkeys and New Hope for Amputees

Apart from sounding super-cool (in a geek-ish way), this new approach harbors multiple advantages. First – a tremendously increased processing power. Thanks to mother nature (or depending on what you believe), our brain proves to be quite efficient in processing data. The new generation of computers will benefit from that very same system. Second – the new chips will be considerably more power efficient, suggesting they may be used in places where power support is an issue. We may expect an additional decrease in electronic-chip sizes as well.

And lastly… did I already mention that this new architecture sounds super cool?

Sources:

http://news.boisestate.edu/update/2013/08/14/research-team-building-a-computer-chip-based-on-the-human-brain/

http://en.wikipedia.org/wiki/Memristor

https://twitter.com/thenanoclast

http://www.frogheart.ca/?tag=cif-small-realizing-chip-scale-bio-inspired-spiking-neural-networks-with-monolithically-integrated-nano-scale-memristors

http://www.sciencedaily.com/releases/2013/08/130814144705.htm

http://www.cbronline.com/news/tech/hardware/microelectronics/researchers-working-on-chip-that-mimics-human-brain-190813

https://wondergressive.com/2013/06/16/of-cyborg-monkeys-and-new-hope-for-amputees/

https://wondergressive.com/2013/06/12/neocortex-how-human-memory-works/

https://wondergressive.com/2012/10/13/electronic-brain-implants-increase-intelligence/

Amsterdam’s Interesting Housing Solution

January 8, 2013 / esfein / Leave a comment

vectroave.com

Amsterdam has implemented an amazing green architecture technique to deal with limited space and lower income needs: Retired shipping containers. These small houses can even be used for temporary disaster relief housing. Not only that but, According to figures from SG BLOCKS, a New York-based shipping container builder,

fitting a container for housing use takes only one-twentieth the amount of energy of reprocessing the same amount of steel—and results in an additional hundred years of lifetime.

So it’s more green than recycling the shipping containers, but it also costs less than constructing new housing.

Companies that build modular buildings from shipping containers claim savings of 20 to even 50 percent of traditional construction costs.

Not to mention they’re practically real life legos for people to live in. BAM!

Sources:

http://environment.nationalgeographic.com/environment/sustainable-earth/pictures-amsterdam-shipping-container-homes/#/rio-20-un-climate-conference-shipping-container-homes-sitting_54416_600x450.jpg

http://www.sgblocks.com/the-sg-blocks-advantage/better-for-the-environment/

Enslaved Ants Regularly Stage Rebellions

October 13, 2012 / esfein / 1 Comment

Ants that become enslaved by other ants naturally and regularly rebel against their captors.

Ants are notorious for making sprawling networks of city states beneath the ground. They have been observed farming mushrooms, domesticating aphids, and even creating nurseries and learning centers for their young.

Scientists have made a new discovery, further anthropomorphizing ants. Ants all over the United States take other species and colors of ants as slaves, and the slaves very often try to break free, or sabotage the captors’ colony. As usual, truth is more surprising than fiction.

Protomognathus americanus, the American slave maker ant, has evolved to stop foraging for food and instead steal the larvae of other ants and raise them as slaves to forage for food and raise their young. Talk about lazy.

Just like in our society, the enslaved ants don’t just blindly accept their servitude. The slave ants sabotage the colony by killing thousands of the colony’s children. When an ant is newborn, the enslave ant nanny is unable to tell the difference. But once it begins to show signs that it is the same species as its captor, the enslaved ant is quick to brew the poison.

Interestingly, only 27% of slave maker ant pupae survived within colonies in West Virgia, Ohio, and New York. Despite this fatal statistic, the ants continue the slave trade. Somebody call DCFS.

If you are interested in further information regarding the minds of ants check out this mind blowing spectacle. Scientists poured cement into the tunnels of an ant colony, and after waiting for it to harden, excavated many tonnes of earth to analyze the structure of the whole colony. They found a copious amount of roads, sub roads, garbage dumps, fungal gardens, nurseries, and more. Even more amazingly, the tunnels were designed for optimal ventilation, and efficient transportation. Each colony, from an ant’s perspective, is equivalent of building the Great Wall of China.

You are walking on top of thousands of world wonders every day!