Category: Math - ROBERT E DUNN

pascal's triangle

9/21/2023

Blaise Pascal's triangle on the left has eight secrets. One is found by drawing shallow diagonals, revealing the Fibonacci Sequence on the right.

This came up during tutoring. Alexander learned what a perfect number is, a positive integer equal to the sum of its divisors (including one and excluding itself). Six is a perfect number: 6 = 1+2+3. Twenty-eight is a perfect number: 28 = 1+2+4+7+14.

Then we learned that all even perfect numbers are triangular numbers. That is when Alexander reminded me, no, chastised me, about Pascal's triangle. Which boy forgets nothing?

artwork courtesy of Wikipedia and David Tung on Quora

intro to calculus

9/9/2023

Isn’t this better than watching TikTok videos or commercials?

If y = x squared, substitute for x the number 2 and y = 4. Do the same for other numbers, and you will see the parabola forming in Quadrant 1. I liked every single day of K-12, and school is where I wanted to be. I never felt loved in school after that, which explains why I tutor middle and high school, and Alexander. If you are in college and feel the same way, I have no solution. Just persevere. Find a Latin Mass.

pink noise

8/31/2023

Pink noise is fractal. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop.

A 2012 study in the Journal of Theoretical Biology found that steady pink noise reduces brain waves, which increases stable sleep. A 2017 study in Frontiers in Human Neuroscience also found a positive link between pink noise and deep sleep.

Brown noise is hurricane-force wind.

below Fibonacci c. A.D. 1200, 8 billion, not 6.5, fractals, and the Golden Ratio

It's just the twenty-first letter, phi, of the Greek alphabet.

Illuminati is a name assumed by the members of a secret society founded by Adam Weishaupt in 1776.

ca parents union

8/28/2023

Visit the website of the California Parents Union, the place for parents, grandparents, and guardians who are fighting for parental rights and the protection of minors against gender interventions and radical political indoctrination. Tip line available.
californiaparentsunion.com/

Read about a 5th grade teacher in Georgia who decided it was appropriate to teach gender concepts in place of multiplication and binary equations. She read My Shadow Is Purple in class and was fired after parents objected. The book promotes a non-binary lifestyle.

https://pjnewsletter.com/teacher-gender-binary-book-career/?utm_medium=email&utm_source=actengage

Here is the math:

Using the binary* to decimal formula, one can convert a binary number, which is base 2, to a decimal number, which is base 10. If the given binary number is 1101011, using the formula (not shown here), the decimal number is 107.

*Binary is used in the computer world.

The book has a grammar mistake: fully unique. One of my friends said that all children want is recess. He understands children; the teacher and the author do not.

fire tetrahedron

8/25/2023

A triangular pyramid is a geometric shape that has a triangular base and three lateral triangular faces. It has a vertex, the point that is common to all three lateral faces. If all three faces are equilateral, that is, all the sides are of equal length, then such a pyramid is called a tetrahedron. See summer fires in Canada, Greece, and Hawaii.

karat & hanging 10

8/25/2023

A gold karat is 1/24 part of the whole, and the purity of a gold alloy is expressed as the number of the parts of gold it contains. Thus, an object that contains 18 parts gold and 6 parts alloying metal is 18-karat gold, and pure gold is 24-karat gold.

Golden California surfer jargon: hanging 10 means wrapping all ten toes over the edge of the surfboard. Joe B: “I am sitting on the porch putting down some frat water…Just hanging ten and livin’ the dream.” HB: “I thought you were in Tahoe.”

girl math

8/17/2023

Get off TikTok! It is a Chinese Communist Party app mining your personal information, especially selfies, for blackmail. That is why I put no pictures of living relatives or friends on my website. Do real math. See me.

Your Worth

8/11/2023

Assuming you are an American and assuming you are as valuable as an Iranian international criminal, your current worth is $3 billion.

answer checked
https://amgreatness.com/2023/08/11/biden-to-make-6-billion-iranian-prison-swap/?utm_medium=email&utm_source=act_eng&seyid=82407

slicing a rectangle

8/8/2023

How many ways can you cut a rectangular board into four equal parts? Assume the board is a 2x4 or any similar measurement. Alexander was given the problem. You can build a hanging planter with nothing but 2x4s, a pallet, and one of my designs.

The drawing I wanted Alexander to see was the “top right” one because with that one he could see that by halving rectangles again and again, one gets more and more of them.

Rectangles are fractals. https://medium.com/hackerlog/fractals-it-goes-on-and-on-and-on-and-on-and-on-and-on-forever-14cae8b886e6

99

8/6/2023

I chose this problem because the answer is very clever.

There are 99 of you locked in one room. Everyone must choose a number between 1 and 100. You will only survive if no one else chooses the same number as you. Which one do you choose and why? Answered by Gaurav Gupta, Quora, July 20

Frankly, I'm going to assume we can't choose decimal numbers, as that would probably ruin this game and make it completely useless.
Next, I'll assume we have a limited amount of time to pick the number. This means that any coordination between the groups is impossible to achieve. So now I just have to guess, hoping no one chooses my number.

1. The first thing I'm going to do is ignore the spectrum (1-20) and (80-100), simply because most people will automatically turn to these numbers, leaving the numbers in the center relatively intact. We are left with more than spectrum 21 to 79. What to do now? Let me explain.

2. I will also eliminate the remaining numbers that could symbolize birthdays or a day of the month. So, spectrum 21 to 31. There is now a range of 32 to 79.

3. I will now forget all the even numbers because they are most likely to be caught because of the ease of division. Now here are the remaining numbers: 35; 37; 39; 41; 43; 45; 47; 49; 51; 53; 55; 57; 59; 61; 63; 65; 67; 69; 71; 73; 75; 77; 79.

4. I now remove the square numbers and then the numbers divisible by a digit (1 excluded). We then end up with this little list: 37; 41; 43; 47; 53; 59; 61; 67; 71; 73.

5. I only have odd AND prime numbers left, very little used, so I am now one of those who have the best chance of winning. I choose …
41

oppenheimer

8/2/2023

Many years apart, Alexander, nine, and I got as close as Amargosa Valley.
The Grable shot was named after American actress/pinup Betty Grable.

maritime accidents

8/2/2023

image courtesy of Rogelio Barsallo, professional mariner, Quora contributor
B.Sc. in Marine Transportation, United States Merchant Marine

Boxhall's ashes were scattered to sea at 41°46N 50°14W – the position he had calculated as Titanic's final resting place 55 years earlier. The ship had sunk on April 15, 1912. He died on April 25, 1967. Captain Edward Smith, age 62, married and one daughter, did his duty and went down with the ship.

silk

8/1/2023

One silk tie requires 150 Silk cocoons.
One pound of silk requires 2,500 Silk cocoons.
How much silk is in one tie? A tie needs 150 cocoons, so 150/2,500 = .06
That is 6% of a pound, which is .96 ounces, almost one ounce. If that were weed, I would call the cops. Tiny farmers raise 200K to 1 million silkworms at a time. Both are ugly, so I am providing no pics. You can submit a pic of your pretty silk anything.
Egg 10-25 days
Larva/worm 20-33 days
Pupa 10-14 days
Moth 5-10 days

mandelbrot set

7/23/2023

Bill looked at the fractal entry and recommended a YouTube video on the Mandelbrot Set. However, I looked for a shorter video, one more suitable for a short blog entry. The area of Quora that I am part of is Number Theory. I am a student of it. It is not algebra or geometry or other, but a combination of them all and a deeper inquiry into numbers. The demonstration will be two-dimensional with three-dimensional, computer-generated art. In the YouTube video that follows this one, the math teacher locates the Fibonacci Sequence in the Mandelbrot Set. Thank you, Bill. Enjoy.

fractal

7/20/2023

A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. - loop courtesy of fractalfoundation.org

heat wave

7/13/2023

Did you ever think it possible for Greenland to have a heat wave? Well, the hottest day ever recorded, according to records that go back 74 years to 1949, was 74.5℉ (23.6°C). As of June 15, 2023, Greenland has had a near-average melt year. Total melt-day area ranked twenty-third in the 45-year-satellite record with present data. Did you know that Tahiti, near the bottom of the globe, still belongs to France? Water temperature in Tahiti today is 79.9°F. Bathtub.

Alexander and I worked on this problem.

You would feel light, but you would succumb. Mercury has extreme climes. The part facing the sun is extremely hot, whereas the other side is freezing. There is a lack of air. Without a spacesuit, you would survive for two minutes or not even that.

d = R X T

7/6/2023

Here is a math problem Alexander, nine, and I had today. Algebra 1.

A train running 1320 miles in 24 hours starts ½ hours late. How much must it increase its speed to arrive on time?

Because the train starts the trip ½ hours late, it must traverse the entire distance in only 23 and 1/2 hours.

Two versions of the distance, rate, time problem:
(1) D = R x T
(2) average velocity = distance/time

Using the second version...

v = 1320/23.5
v = 56.2 mph

If the train had NOT started late,
v = 1320/24
v = 55 mph

56.2 - 55 = 1.2

So, the train must increase its speed by 1.2 mph over the other trip speed.

perfect squares

7/3/2023

Only those numbers that are perfect squares have an odd number of factors. For example, nine has an odd number of factors: 1, 3, and 9. Sixteen has an odd number of factors: 1, 2, 4, 8, 16. This is the key to solving a puzzle called, “Switching 100 light bulbs”. Dr. Josef Ketzer of Austria posed the problem in the blog post on 6/28/2023, Dividing Square Roots. See if you can find the answer without looking at the answer.

twitter limits

7/1/2023

“Hours after users began reporting the problems, billionaire owner Elon Musk tweeted that the site had applied temporary limits ‘to address extreme levels of data scraping and system manipulation.’

“‘Verified accounts are limited to reading 6,000 posts a day,’ he tweeted. Unverified accounts are limited to just 600. New unverified accounts are at 300 posts a day.”

July 1, 2023, CNN

Who reads 6,000 posts in a day? AI? Math has limits! Maybe Twitter needs a new name, Outer Limits.

CNN shows bias with one word, for everyone knows he is a billionaire.

chart courtesy of onlinemathlearning.org

dividing square roots

6/28/2023

The problem looks simple, but the lesson readies a middle school student for algebra and is placed in the blog because John reviews must-know, pre-Algebra definitions. I have entered several of John’s videos into the blog because this is the ideal way to teach or tutor, unlike the vile teacher in the post, UK Teacher Recorded 6/24/2023.

You can divide the square root of 30 into 10 parts. It will be an approximation, but it's good enough.

transfiguration

6/23/2023

art / geometry

Left
Transfiguration of Jesus, downloaded from Artist Hideout. Artist: Raphael (1483-1520). Date of painting: 1516-1520. Medium: oil on panel. Vatican Museum, in the public domain. https://commons.wikimedia.org/wiki/File:Transfiguration_Raphael.jpg

Right
Lecture Diagram 10: Proportion and Design of Part of Raphael's 'Transfiguration'. Part of the Turner Bequest to the Tate (1856). Author: Joseph Mallord William Turner. Date of diagram: c. 1810. Date/time of photo: 2 January 2013, 16:04:27.
Source:
http://www.tate.org.uk/art/artworks/turner-lecture-diagram-10-proportion-and-design-of-part-of-raphaels-transfiguration-d17134.
Copyright: https://commons.wikimedia.org/wiki/File:Proportion_and_Design_of_Part_of_Raphael%27s_Tranfiguration.jpg

what is Ph?

6/16/2023

One sees pH on product labels. It stands for potential hydrogen and describes the acid-alkaline ratio of substances. Remember that ratio is something to something.

diagram courtesy of expii.com

Two words in the diagram explained:

logarithm (connotation outside math, baroque)
How does one find the log of a number? The logarithm of a number is the power to which 10 must be raised to equal that number. Some examples are

10 squared = 100, therefore log10 of 100 = 2
10 cubed = 1000, therefore log10 of 1000 = 3

aqueous (connotation outside science, baroque)
Aqueous is an adjective meaning “of or containing water.”

9 words & 270

6/16/2023

Nine words invented by mistake: algorithm; sneeze; tornado; culprit; pea; ammunition; sherry; sashay; varsity. Two-minute read about how they happened: https://www.wordgenius.com/how-were-these-words-invented-by-mistake/Xr0yWBPAJQAG8xAP?utm_source=blog&utm_medium=email&utm_campaign=1828558122

An owl can swivel its head 270 degrees. 270/90 = 3 (quadrants)

diagram courtesy of study.com

combinations dispute

6/15/2023

Alexander, nine, and I had a dispute over a combinations problem. In fact, we were both wrong. I went home and checked my sources.

Combinations
There are 91 elements to choose from, and 4 elements are chosen. In English, if you have 91 students and choose four at a time, how many combinations are there?

Calculation:
Formula n!/k!(n−k)!

Two examples of a factorial:
91! = 91x90x89x88… (and so on)
4! = 4x3x2x1

Where n = 91 and k = 4

C₄(91) = (91/4) = (91!/4!(91−4)! = 91x90x89x88/4x3x2x1 = 2672670

The number of combinations is 2,672,670.

rationalizing the denominator

6/9/2023