Completely New Math Corollary

Use this forum to discuss the philosophy of science. Philosophy of science deals with the assumptions, foundations, and implications of science.
Post Reply
Kane Jiang
Posts: 42
Joined: August 8th, 2019, 5:28 am

Completely New Math Corollary

Post by Kane Jiang »

Here is a completely new math corollary I invented.

For any mathematical average, the sum of how much larger than the average the numbers above are must equal the sum of how much smaller than the average the numbers below are.

Mathematical averages are usually calculated by adding all the numbers up and dividing the sum by how many numbers there are. The mathematical average of a group of numbers indicates the number overall the overall group is closest to.

Now an example of the corollary:

For example, if the numbers are 75 and 79, the average is 77 because 79 is 2 larger than 77 and 75 is 2 smaller than 77. This is common sense.

But what if you have 3 numbers? Let's say you have 74, 78, and 79. The average is 77 because 78 is 1 larger than 77 and 79 is 2 larger than 77 and 2 + 1 = 3. 74 is 3 smaller than 77 so 3=3. You can use guess and check until you arrive at the average if you're not sure which number to pick.

This method can help you calculate means of numbers that are close together faster in your head without adding up the numbers or the one's digits of the numbers. It will work on any mean.

Derivation of the corollary:
(Sum of n) / x = y
x is the number of numbers, y is the mean
Sum of n = x * y
Sum of n - x * y = 0
(Sum of n) /x - y = 0
(N1/x - y) + (N2/x - y) + ... = 0
Now put all the numbers below on one side and all the numbers above on the other side...
and that is a fail; maybe it's really a postulate instead?

2nd attempt
N1 - y + N3 - y = y - N2
N1 + N3 + N2 = 3y
(N1 + N3 + N2)/3 = y
If anything, the mean formula is derived from my corollary.

I'm not sure right now if it's a postulate or corollary, but I think it's a postulate and the common mean formula is a corollary to the postulate.

I'll get back to you on that one. In the meanwhile, feel free to post.

Copyright 2019 by Yukang Jiang
User avatar
h_k_s
Posts: 1243
Joined: November 25th, 2018, 12:09 pm
Favorite Philosopher: Aristotle
Location: Rocky Mountains

Re: Completely New Math Corollary

Post by h_k_s »

Kane Jiang wrote: August 9th, 2019, 4:36 pm Here is a completely new math corollary I invented.

For any mathematical average, the sum of how much larger than the average the numbers above are must equal the sum of how much smaller than the average the numbers below are.

Mathematical averages are usually calculated by adding all the numbers up and dividing the sum by how many numbers there are. The mathematical average of a group of numbers indicates the number overall the overall group is closest to.

Now an example of the corollary:

For example, if the numbers are 75 and 79, the average is 77 because 79 is 2 larger than 77 and 75 is 2 smaller than 77. This is common sense.

But what if you have 3 numbers? Let's say you have 74, 78, and 79. The average is 77 because 78 is 1 larger than 77 and 79 is 2 larger than 77 and 2 + 1 = 3. 74 is 3 smaller than 77 so 3=3. You can use guess and check until you arrive at the average if you're not sure which number to pick.

This method can help you calculate means of numbers that are close together faster in your head without adding up the numbers or the one's digits of the numbers. It will work on any mean.

Derivation of the corollary:
(Sum of n) / x = y
x is the number of numbers, y is the mean
Sum of n = x * y
Sum of n - x * y = 0
(Sum of n) /x - y = 0
(N1/x - y) + (N2/x - y) + ... = 0
Now put all the numbers below on one side and all the numbers above on the other side...
and that is a fail; maybe it's really a postulate instead?

2nd attempt
N1 - y + N3 - y = y - N2
N1 + N3 + N2 = 3y
(N1 + N3 + N2)/3 = y
If anything, the mean formula is derived from my corollary.

I'm not sure right now if it's a postulate or corollary, but I think it's a postulate and the common mean formula is a corollary to the postulate.

I'll get back to you on that one. In the meanwhile, feel free to post.

Copyright 2019 by Yukang Jiang
I think you will love Statistics when you get to college.

Statistics already has concepts of the mean, the median, and the mode, together with standard deviations from the same.

It sounds like you have discovered the standard deviation on your own in a different way.
Kane Jiang
Posts: 42
Joined: August 8th, 2019, 5:28 am

Re: Completely New Math Corollary

Post by Kane Jiang »

h_k_s wrote:I think you will love Statistics when you get to college.

Statistics already has concepts of the mean, the median, and the mode, together with standard deviations from the same.

It sounds like you have discovered the standard deviation on your own in a different way.

Well, I already have a bachelor's degree and I discovered this formula when I was in middle or high school, although I didn't tell anyone.

It would be useful on the SAT's, especially when you have multiple choice answers so you wouldn't even need to guess and check?
I've never heard of it being used on the SAT, so I'm pretty sure it's original and that's why I posted it here.
Kane Jiang
Posts: 42
Joined: August 8th, 2019, 5:28 am

Re: Completely New Math Corollary

Post by Kane Jiang »

h_k_s wrote:I think you will love Statistics when you get to college.

Statistics already has concepts of the mean, the median, and the mode, together with standard deviations from the same.

It sounds like you have discovered the standard deviation on your own in a different way.
Well, I already have a bachelor's degree and I discovered this formula when I was in middle or high school, although I didn't tell anyone.

It would be useful on the SAT's, especially when you have multiple choice answers so you wouldn't even need to guess and check?
I've never heard of it being used on the SAT, so I'm pretty sure it's original and that's why I posted it here.
User avatar
h_k_s
Posts: 1243
Joined: November 25th, 2018, 12:09 pm
Favorite Philosopher: Aristotle
Location: Rocky Mountains

Re: Completely New Math Corollary

Post by h_k_s »

Kane Jiang wrote: August 13th, 2019, 3:17 pm
h_k_s wrote:I think you will love Statistics when you get to college.

Statistics already has concepts of the mean, the median, and the mode, together with standard deviations from the same.

It sounds like you have discovered the standard deviation on your own in a different way.
Well, I already have a bachelor's degree and I discovered this formula when I was in middle or high school, although I didn't tell anyone.

It would be useful on the SAT's, especially when you have multiple choice answers so you wouldn't even need to guess and check?
I've never heard of it being used on the SAT, so I'm pretty sure it's original and that's why I posted it here.
Did you take any Statistics courses while in college? Your algorithm sounds exactly like the "standard deviation" function in Stats.
Kane Jiang
Posts: 42
Joined: August 8th, 2019, 5:28 am

Re: Completely New Math Corollary

Post by Kane Jiang »

What standard deviation function? I did take a stats course but my algorithm was devised before I took the course. Can you tell me what formula you’re referring to?
Kane Jiang
Posts: 42
Joined: August 8th, 2019, 5:28 am

Re: Completely New Math Corollary

Post by Kane Jiang »

h_k_s wrote:Your algorithm sounds exactly like the "standard deviation" function in Stats.
If you mean this formula sqrt(sum of (x - mean))^2/n), I don't think that formula has any correlation with my algorithm. For one, I also use mean - x in my algorithm and there are no square roots or exponents. I also don't divide by anything?
Post Reply

Return to “Philosophy of Science”

2023/2024 Philosophy Books of the Month

Entanglement - Quantum and Otherwise

Entanglement - Quantum and Otherwise
by John K Danenbarger
January 2023

Mark Victor Hansen, Relentless: Wisdom Behind the Incomparable Chicken Soup for the Soul

Mark Victor Hansen, Relentless: Wisdom Behind the Incomparable Chicken Soup for the Soul
by Mitzi Perdue
February 2023

Rediscovering the Wisdom of Human Nature: How Civilization Destroys Happiness

Rediscovering the Wisdom of Human Nature: How Civilization Destroys Happiness
by Chet Shupe
March 2023

The Unfakeable Code®

The Unfakeable Code®
by Tony Jeton Selimi
April 2023

The Book: On the Taboo Against Knowing Who You Are

The Book: On the Taboo Against Knowing Who You Are
by Alan Watts
May 2023

Killing Abel

Killing Abel
by Michael Tieman
June 2023

Reconfigurement: Reconfiguring Your Life at Any Stage and Planning Ahead

Reconfigurement: Reconfiguring Your Life at Any Stage and Planning Ahead
by E. Alan Fleischauer
July 2023

First Survivor: The Impossible Childhood Cancer Breakthrough

First Survivor: The Impossible Childhood Cancer Breakthrough
by Mark Unger
August 2023

Predictably Irrational

Predictably Irrational
by Dan Ariely
September 2023

Artwords

Artwords
by Beatriz M. Robles
November 2023

Fireproof Happiness: Extinguishing Anxiety & Igniting Hope

Fireproof Happiness: Extinguishing Anxiety & Igniting Hope
by Dr. Randy Ross
December 2023

Beyond the Golden Door: Seeing the American Dream Through an Immigrant's Eyes

Beyond the Golden Door: Seeing the American Dream Through an Immigrant's Eyes
by Ali Master
February 2024

2022 Philosophy Books of the Month

Emotional Intelligence At Work

Emotional Intelligence At Work
by Richard M Contino & Penelope J Holt
January 2022

Free Will, Do You Have It?

Free Will, Do You Have It?
by Albertus Kral
February 2022

My Enemy in Vietnam

My Enemy in Vietnam
by Billy Springer
March 2022

2X2 on the Ark

2X2 on the Ark
by Mary J Giuffra, PhD
April 2022

The Maestro Monologue

The Maestro Monologue
by Rob White
May 2022

What Makes America Great

What Makes America Great
by Bob Dowell
June 2022

The Truth Is Beyond Belief!

The Truth Is Beyond Belief!
by Jerry Durr
July 2022

Living in Color

Living in Color
by Mike Murphy
August 2022 (tentative)

The Not So Great American Novel

The Not So Great American Novel
by James E Doucette
September 2022

Mary Jane Whiteley Coggeshall, Hicksite Quaker, Iowa/National Suffragette And Her Speeches

Mary Jane Whiteley Coggeshall, Hicksite Quaker, Iowa/National Suffragette And Her Speeches
by John N. (Jake) Ferris
October 2022

In It Together: The Beautiful Struggle Uniting Us All

In It Together: The Beautiful Struggle Uniting Us All
by Eckhart Aurelius Hughes
November 2022

The Smartest Person in the Room: The Root Cause and New Solution for Cybersecurity

The Smartest Person in the Room
by Christian Espinosa
December 2022

2021 Philosophy Books of the Month

The Biblical Clock: The Untold Secrets Linking the Universe and Humanity with God's Plan

The Biblical Clock
by Daniel Friedmann
March 2021

Wilderness Cry: A Scientific and Philosophical Approach to Understanding God and the Universe

Wilderness Cry
by Dr. Hilary L Hunt M.D.
April 2021

Fear Not, Dream Big, & Execute: Tools To Spark Your Dream And Ignite Your Follow-Through

Fear Not, Dream Big, & Execute
by Jeff Meyer
May 2021

Surviving the Business of Healthcare: Knowledge is Power

Surviving the Business of Healthcare
by Barbara Galutia Regis M.S. PA-C
June 2021

Winning the War on Cancer: The Epic Journey Towards a Natural Cure

Winning the War on Cancer
by Sylvie Beljanski
July 2021

Defining Moments of a Free Man from a Black Stream

Defining Moments of a Free Man from a Black Stream
by Dr Frank L Douglas
August 2021

If Life Stinks, Get Your Head Outta Your Buts

If Life Stinks, Get Your Head Outta Your Buts
by Mark L. Wdowiak
September 2021

The Preppers Medical Handbook

The Preppers Medical Handbook
by Dr. William W Forgey M.D.
October 2021

Natural Relief for Anxiety and Stress: A Practical Guide

Natural Relief for Anxiety and Stress
by Dr. Gustavo Kinrys, MD
November 2021

Dream For Peace: An Ambassador Memoir

Dream For Peace
by Dr. Ghoulem Berrah
December 2021