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    • 2013 Publication

THE CURVE SHAPES OF NATURE: 
Bell Curve Shape and Asymptotically Descending Curve Shape

Editor's Note: Sae Rheen K. ('16) and her father, Isaac K. wrote this submission about two different geometric curves.
For ages since ancient times people with curious minds studying various phenomena in nature have long known that typically 2 types of curve shapes dominate their observations: bell shape and asymptotically descending shape.

The bell shape cure is given the name Gaussian distribution, named after the 18th century German mathematician Karl Friedrich Gauss.  Gauss introduced a mathematical model widely used wherever statistics is used.  Gaussian, a bell shaped curve, describes a distribution of events that occur due to random nature.

As an example, let’s imagine we drop 1,000 of perfectly round glass balls in a sequence from 10th floor window of an apartment building.   As the ball travels before hitting the ground it experiences the wind blowing directly against it.

Picture
Thus there are 2 factors working against the ball, the force of gravity pulling it towards the ground and the wind blowing in all directions and the direction in which the wind affects the ball is in random direction.  After the 1,000th ball is dropped, if you count the spot of the ground where the balls hit when they landed most of the balls would have fallen right at the center and gradually spread outward as shown in the graph above.  Now imagine we now glue a feather around each ball and repeat the same experiment.  How would the plot of the number of balls over the area where the balls hit look like?  It would look similar the one above, except, the bell shape would have spread out more widely since the effect of the wind would be more pronounced as the feather on the ball would offer more resistance to the wind.

Asymptotically descending curve shape is found while scientists were studying the nuclear radiation.  As they observed that when the nucleus decays so that a positively charged particle leaves the nucleus in the form of radiation they discovered that the rate at which the nucleus decays is directly proportional to the 

mass of the remaining matter.  Thus a differential equation such as the following is developed:  
Picture
where N is number of particles in the matter.  
Solving this differential equation, one can express N as following:
Picture
Where N0 is the number of particles at initial time (t=0) and putting this equation as
Picture
Again, taking log on both sides of this equation and solving for time t as t t =ln(1/2)*l represents so called half life of the particle, meaning the time it takes for the matter to decay by half.  The plot of this graph looks like following for the case of radio active isotope of carbon, so called Carbon-14:

Picture
This form of the differential equation occurs not only in nuclear Physics but even in economics an observation of the rate at which corporations surviving follows the same pattern, so that when this differential equation is solved for N shows that the total number of corporation slowly decays to smaller number over time.  Well, the graph above for Carbon-14 is actually used to estimate the age of matter believed to have existed many years in history. And this pattern of exponential decay keeps on occurring around us.

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  • Home
  • Who We Are
  • HOW TO SUBMIT
  • Past Publications
    • 2019 Publication >
      • Scientific Research
      • Mathematical Exploration
      • Scientific Exploration
      • Computer Science
    • 2018 Publication >
      • Artistic Creations
      • Historical and Current Explanations
      • Mathematic and Scientific Exploration
      • Scientific Research
    • 2017 Publication >
      • Artistic Creations
      • Historical and Current Explanations
      • Mathematic and Scientific Exploration
      • Reactions and Responses
      • Scientific Research
    • 2016 Publication >
      • Historical and Current Explanations
      • Mathematic and Scientific Explorations
      • Scientific Research
      • Reactions and Responses
      • Artistic Creations
    • 2015 Publication >
      • Historical and Current Explanations >
        • Bell Curves
        • Birds Vs. Turbines
        • Energy in the Obama Era
        • The Future of Neuroscience
        • Gender Gap in Math
        • GMOs--Yes or No?
        • The History of Minecraft: How a Swedish Indie Game Came to Dominate the World
        • The Effect of Prozac on the Brain
        • Philae Lander's Discovery of Organic Molecules
        • Advantages and Disadvantages of Wind Turbines
        • Your Own Worst Enemy: An Overview of Lupus
        • The Methylhex Ban
        • The Effect of Lyme Disease on the Immune system
        • Infectious Mononucleosis
        • Replacing CFCs
        • The Switch
      • Mathematic and Scientific Explorations >
        • The 43rd Figure
        • The Clock
        • The Collatz Conjecture
        • Constructing a Soccer Ball
        • Determining how Ballparks Affect Batter's Ability to Create Hits
        • The Rotating Conundrum
        • Pythagorean Puzzle
        • Mathematic and Scientific Explorations
        • Kinetics Lab
        • Math in the Restaurant Business
        • Math as a Vessel for Social Change
        • Sustainability of Bottled Vs. Tap Water
        • Thoughts on the Lottery
        • Understanding Player Efficiency Rating
      • Scientific Research >
        • Communicating With Computers
        • The Mystery of Asthma
        • The Nanoscopic War Against Cancer
        • Phytochemistry
        • Solving the energy crisis with Intermediate Band Solar Cells
        • A Pain That Never Ends
        • Rapamycin Resistance
        • Ampacity of a Single Core Horizontal Cable
        • Morphological Properties of Texting Acronym Formation
        • cGAS and STING Expression
      • Reactions and Responses >
        • Can Humans Survive the Climate Crisis?
        • My Experience as a Teacher's Assistant
        • Ted Talk Responses
        • Teens For Food Justice
      • Artistic Creations >
        • Chandelier
        • Deltoidal Hexacontrahedon
        • Dodecahedron Card Trick
        • Eye of the Triangle
        • Free Radric Delantic Davis
        • The Grid
        • What Does A Randomly Composed Song Sound Like?
        • Science Wing Mural
    • 2014 Publication >
      • Cover Photo
      • Artistic Creations >
        • Art Using the Fibonacci Sequence
        • Computer Generated Architecture and Designs
        • Mathematical Landscape
        • Math Art
        • Math in Music
      • Historical and Current Explanations >
        • Algae Bio-Fuel
        • An Energy Alternative
        • Clean Energy In Transportation
        • Calorie Restriction
        • Creating Energy in the Modern World
        • Dietary Intervention Impact on Gut Microbial Gene Richness
        • Earthly Applications for NASA Technology
        • Explaining Relative Motion
        • Exploring Artificial Inteligence
        • Gamma Function
        • How Leaves Work
        • Hydrogen Fuel Cells
        • Music and Brain Development
        • Programming Calculators
        • The Science of Microsatellites
        • Sci-Fi Taser
        • Sloane's Gap
        • Sustainable Energy: Why Some Ideas Shine Brighter than Others
        • Understanding The Galvanic Cell
        • The Virus: Our Unforeseen Philosopher's Stone
        • What Are Fuel Cells and How Do They Work?
      • Mathematic and Scientific Explorations >
        • Astrocytes Expressing ALS-Linked Mutated SOD1 Release Factors Selectively Toxic to Motor Neurons
        • Big Bang
        • Dictyostelium Discoideum
        • The Future of Solar Cell Technology
        • And Many More...
      • Reactions and Responses >
        • Alternative Energy Sources, New but Unused
        • An Insight Into the Curious World of Ethnobotany
        • Challenging What We Think We Know
        • The Current State of American Education
        • Discovering New Numbers
        • Interview With an Architect
        • Life of Pi Response
        • Mathematical Art Video Commentary
        • Missing from Science Class
        • The Museum of Math
        • The Inside Scoop on a Real Mathematician
    • 2013 Publication