Category: Math

pentecost 2033

3/18/2023

The date is June 5, 2033. On that Sunday, the Catholic Church will be 2,000 years old. Left is a fresco of the Holy Ghost in the Karlskirche, Viennese Church of St. Charles, the last great work of the Baroque architect Johann Bernhard Fischer von Erlach. Completed in 1739, it was built when Emperor Charles VI made a vow during a plague. The church is dedicated to the Habsburg emperor’s namesake, St. Karl Borromäus (St. Charles Borromeo), whose life and works are depicted on the two giant columns next to the entrance portal. The lavish dome frescoes are by Johannes Michael Rottmayr and cover 1,250 m². Multiply the area value by 10.764, and the result is approximately 13,455 square feet.

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americanisms

3/7/2023

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Riffraff – The Mississippi River was the main thoroughfare from north to south. Riverboats carried passengers and cargo, but they were expensive, so most people used rafts. Everything had the right of way over rafts, which were considered cheap. The steering oar was called a “riff”, which transposed into “riffraff.”

Showboat – This was a floating theater built on a barge that was pushed down the Mississippi. The boat did not have an engine, and the boat was gaudy and attracted attention, which is why we say that someone who is the life of the party is “showboating.”

Barge in – Heavy freight was moved along the Mississippi in large barges pushed by steamboats. The barges were hard to control and would sometimes swing into piers or other boats. People would say, “They barged in.”

Shot of whiskey – In the old west a .45 cartridge for a six-gun cost 12 cents, and so did a glass of whiskey. If a cowhand was low on cash, he would often give a bartender a .45 cartridge for a drink. This became known as a “shot of whiskey.”

Math trivia – No piece of paper can be folded in half more than seven times.

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counting trees

3/3/2023

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The following comes from interestingfacts.com and is so unexpected that I copied the entire entry. The editors do an excellent job resourcing and summarizing facts. The three dots are there because I cut out the first sentence referring to arrogant Carl Sagan.

“… there may be more trees on Earth than stars in the Milky Way galaxy. [that’s where we live] The theory stems from a 2015 study that attempted to determine how many living trees could be found on the planet, by estimating the number of trees living in different environments.

“Tropical and subtropical forests appear to have 43% of the world’s tree population, nearly double that of frosty boreal forests found in places such as Canada, Russia, and Norway. Other regions, including the temperate biome (central Europe and the U.S. Northeast), generally have the fewest number of trees.

“The combined estimates per zone lead some scientists to believe that Earth is home to roughly 3 trillion trees. Compared to NASA’s estimate of more than 100 billion stars in the Milky Way, it appears that trees far outnumber the Milky Way’s sparkling orbs.

“However, the scientific community acknowledges that we’ll likely never know the true number of stars in the sky or how many trees are rooted in the Earth, because there are too many factors at play.

“Astronomers can guess at the number of stars by observing how the galaxy rotates and calculating its mass, though not all stars are visible from Earth, and it’s impossible to count them individually to confirm the math.

“On Earth, humans cut down 15 billion trees annually but replace some, with an estimated 1.3 billion saplings produced in the U.S. each year in the hopes of balancing the count. After all, even if we have trillions of them, each tree on the planet is precious.”

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parallax

3/1/2023

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Alexander, nine, and I discussed parallax. I thought that parallax was in a stealth fighter jet, but no. Parallax has to do with our perception of a distant object, such as a jet. Try this. Put your finger in front of you and look at an object. I chose a picture on the wall. I closed my left eye and then my right eye, and the finger moved to the right when I closed my right eye. We said we would teach each other about parallax.

using the sexagesimal system, not the decimal system

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involute

3/1/2023

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The tools needed are a protractor, compass, and ruler; a mini drafter is recommended. Alternate meaning of involute - involved or intricate. “From the second chapter to the end, the detective novel grew more and more involute.”

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moon drift

2/27/2023

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“In 1969, NASA’s Apollo missions installed reflective panels on the moon. These have shown that the moon is currently moving 3.8 cm away from the Earth every year.” The USA is one of the few countries still using the Imperial system of measurement, where things are measured in feet, inches, pounds, ounces, and so forth. Divide the length value by 2.54. Thus, 3.8/2.54 = 1.49606299. Round up to a tenth, which is 1.5, or 1 ½ inches. https://www.space.com/moon-drifting-away-from-earth-2-5-billion-years

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gibbous

2/24/2023

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Gibbous, pronounced with a hard g as in gallows, is an adjective that is used when speaking of the Moon and refers to the observable, illuminated part greater than a semicircle and less than a circle.

Waxing means "getting bigger", and waning means "getting smaller". New Moon means the start of the phases and you can't see it from Earth, because the Moon is located between the Sun and the Earth and no light is being reflected at us. image courtesy of starlust.org

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math 8

2/23/2023

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Here is eighth grade math at St. Gertrude School, Madeira, OH, which is attached to the Dominican church that US Senator Vance attends, northeast of Cincinnati. The curriculum is a blend of basic math and introductory algebra and geometry necessary for the SSAT/HSPT private high school entrance exams. I recommend those prep books for homeschoolers, too. Aside from gender, CRT, and BLM shaming, anywhere that might occur, modern educational goals are at least keeping pace with my own schooling or better. Set the highest standards and help strugglers.

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euler

2/19/2023

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I forgot what a logarithm is, so I checked. A logarithm is the power to which a number must be raised to get some other number. For example, the logarithm of 100 is two, because 10 to the power of two is 100. Thus, written mathematically, log 100 = 2. That's all.

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bee geometry

2/17/2023

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Bees make hexagonal cells. A hexagon has six sides, six edges, and six vertices. The sum of the interior angles is 720 degrees (6 x 120).

A hexagon has nine diagonals. The formula for the number of diagonals is n(n-3)/2, where n represents a side. If there are six sides, by using the formula, we determine that there are nine diagonals: 6(6-3)/2 = 9.

image above courtesy of study.com
Fr. Pierre Jacobs, S.J., taught me geometry in 10th grade.

Observed bee geometry arises only if cells are previously arranged in a way that
each one is surrounded by six other similar cells.

Caption Honeycomb of Western honey bees (Apis mellifera) with eggs and larvae. Date of photo 22 April 2007. Author Waugsberg (talk · contribs). Image selected as picture of the day on Wikimedia Commons for 14 March 2008.

This is a featured picture; members of the community have identified it as one of the finest images on the English Wikipedia, adding significantly to its accompanying article. https://en.wikipedia.org/wiki/File:Bienenwabe_mit_Eiern_und_Brut_5.jpg

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balloon shoot down

2/14/2023

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verbal phrase of shoot
The video looks like a combination of real-time and file footage of F-22 Raptors, the close-ups.

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latin mass chuckle

2/13/2023

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There is a screaming baby. Skip to about 16 minutes and find out why I put up this video.

St. Stephen Cleveland. Father Bede [pronounced bead] Kotlinski, OSB, teaches classical languages at Benedictine High School in Cleveland, and his ‘sweeping gestures’ and loud voice, despite the laryngitis, are perfect for an all-boys sch0ol.

We had a little hiccup in our parish bulletin on Sunday. It read Sexuagesima Sunday II. Uh...that should be Sexagesima, a fraction based on sixtieths, as in the divisions of time, angles, and geographic coordinates. The Latin word for six is sex, and 60 is sexaginta.

Sexagesimal, also known as base 60 or sexagenary, is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form—for measuring time, angles, and geographic coordinates. - Wikipedia (and for our liturgical calendar)

An analog clock has three hands. The short hand indicates the hour, the long hand indicates the minute of the current hour, and the thinnest hand indicates the second of the current minute. I have one in the house that runs on a battery in case there is a blackout.

Because of digitalization, young students today struggle with this concept. Any excuse, even math, to put up the Latin Mass? Altar boys have nothing from which to read. Even the little guys as young as seven, after First Holy Communion, are eligible and memorize everything to pass. St. Stephen Sacramento has 110, base 10.

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subterfuge

2/8/2023

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Can. 87 §1. A diocesan bishop, whenever he judges that it contributes to their spiritual good, is able to dispense the faithful from universal and particular disciplinary laws issued for his territory or his subjects by the supreme authority of the Church. He is not able to dispense, however, from procedural or penal laws nor from those whose dispensation is specially reserved to the Apostolic See or some other authority.

A bishop received the following from the Vatican: “… requests him to ‘make it right’ by petitioning for a dispensation based on further information the … [Vatican] required -- including information on how many attend the TLM [traditional Latin Mass] and how the priest intends to lead them eventually to the Novus Ordo. … There it is. There is no need to listen to Anthony this time, because I summarized him in three words.

Anthony is like a centrifuge, a machine with a rapidly rotating container that applies centrifugal force to its contents, typically to separate fluids from solids. The mathematical expression is F = M x W squared x R, where F represents the centrifugal force, m = mass, w = angular velocity, and r = distance from the origin. With this kind of force, Anthony separates lies from truth.

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cnn vs fox

2/1/2023

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Nielsen ratings Jan. 16, 2023, through Jan. 22, 2023: CNN News – 444,000 viewers in primetime; Fox News – 2,000,000 million viewers in primetime. For every one person watching CNN, there are four persons watching Fox.

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azimuth

1/21/2023

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Once you have had some trigonometry, you can find azimuth. Though spaceship instruments automatically calculate azimuth, space explorers must understand what it means.

The cosine function in a triangle is the ratio of the length of the adjacent side to the length of the hypotenuse. The cosine function is one of the three main trigonometric functions, and it is itself the complement of sine (co + sine).

I’m watching a science fiction film from 1961, and the piloting astronaut calls out the azimuth reading.

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glaciers

1/2/2023

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About 500 glaciers out of 200,000 have disappeared in the last 50 years.
500/200,00 = .0025
.0025 X 100 = 0.25%
0.25% = 1/4 of 1%

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exponent properties

12/3/2022

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Memorize your times tables up to 20. Solutions come faster. Gotcha! You can't shortcut the solution by subtracting the exponents, as in exponent 20 minus exponent 2 (4 being 2 squared). Subtracting the bases results in zero. Don't go there.

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power of x

11/23/2022

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One could have guessed two and been right, but this solution is more like a proof demonstrating the use of the quadratic equation, root quattuor, Latin for four because there are four terms, including the zero. I have a friend whose last name is Ekk. If one saw his family approaching, one could say, “Here come the Ekks.” X

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square root of -9

11/12/2022

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The square root of -9 is 3i. What is i? The answer has to do with complex numbers, not just with the real numbers on the number line. So, i is an imaginary number. For an explanation, see https://www.youtube.com/watch?v=q-9wUxUbi1U

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chess

11/11/2022

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Catholic bishops worldwide 5,600
Catholic priests worldwide 416,000 (rounded)
5,600 + 416,000 = 421,600
5,600/421,600 = .01328273
The odds of a Catholic priest becoming a bishop are 5,600 to 421,600.
Approximately 1% of Catholic priests will become a bishop.

It’s a lopsided chess game right now with small numbers of pawns (priests) trying to hem in Francis, the bad bishop.

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nth root

10/28/2022

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Alon Amit, PhD in Mathematics and Mathcircler, gives a fantastic answer to the following question: What is the practical usefulness of learning the Nth root of a number? My soon-to-be 7th grade son asked me: If I/we could think of good reasons for finding 2nd and 3rd root but not the Nth. Any good explanations? Alon relates his math to the piano and a bicycle wheel. Interested? Read the deal … Quora.
https://www.quora.com/What-is-the-practical-usefulness-of-learning-the-Nth-root-of-a-number

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uncountable infinity

10/25/2022

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Richard Ferrara, Quora contributor, Software Engineer, Catholic, conservative Republican, Scrabble player, MS Mathematics & Physics, University of Copenhagen (1971), MSc Mathematics, University of Bristol (1990)

What is an uncountable infinity?

Let’s say you die and go to Hell.

You insist that there has been some mistake and file an appeal with Saint Peter. He convenes a panel of archangels to consider your case.

Eventually, a compromise is reached: you can win your soul back, but to do so, you must beat the devil in a guessing game.

I.
Here’s how it works: the devil writes down a whole number on a piece of paper. This number never changes. It can be any positive whole number — there is no upper limit. It can be 52, a trillion, a googolplex, whatever. [Nine-year-old Milton Sirotta coined the term googol, 10 to the 100 power, and then proposed the term googolplex to be “one, followed by writing zeroes until you get tired.”]

Each day you get one guess. If you correctly pick the devil’s number, you go free. Otherwise, you’re stuck there for another day.

(We assume that you have some foolproof way of keeping track of what numbers you’ve previously chosen, the piece of paper is big enough to fit any number, the devil doesn’t cheat and change it, etc.)

What do you do?

Well, the bad news is that there’s no telling how long you’ll be in perdition. But the good news is that a simple strategy will get you free.

On the first day you guess one. If that’s the devil’s number, great, you’re free. If not, then on the second day you guess 2, then 3, 4, 5, and so on.

It may take eons, but eventually you will reach the right number and escape. That’s because even though there are an infinite number of positive integers, it’s a countable infinity — a set whose members can be arranged in order so that you can hit every one of them. The devil cannot pick a number so high or complex that you will never reach it.

II.
Now let’s change the rules of the game: this time the devil can pick any integer (positive, negative, or zero).

Obviously, you can’t follow the same strategy, because you will miss all the negative numbers. However, you can still win. Just start with zero, then plus 1, then minus 1, plus 2, minus 2, and so on.

Even though it looks like more choices have been added, the result is still a countable infinity. In math terminology, we say that the cardinality of the set hasn’t changed.
(It’s called “aleph-null” if you want to get technical.)

III.
Now let’s change the rules again: this time the devil can pick any rational number (i.e., any number that can be expressed as a fraction).

At first glance, it looks like the game is now unwinnable. What’s the fraction with the smallest value greater than zero? One half? No, one third is less. And one fourth is less than that. And what’s the first number greater than one fourth? 2/7? 3/11?

You are in trouble now.

Or are you?

See, there’s a trick: although you need to find some way to order your guesses, you don’t necessarily need to order them by value.

A fraction is just a pair of numbers: a numerator and a denominator.

Imagine those two numbers as X and Y coordinates on a plane. You can now win the game by starting from the origin and working outward in a spiral.

First you guess all the fractions whose numerator and denominator add up to 1. There’s only one of them: 0/1.

Next, the ones that add up to 2, which are 0/2 and 1/1.

Then 0/3, 1/2, 2/1. And so on.

It took some thinking this time, but once again you’ve escaped.

IV.
Okay, one more: this time the devil can pick any irrational number.

It can be pi, or e [Euler’s number, an irrational number with a non-recurring decimal that stretches to infinity], or the 20th root of a billion, or the square of the cosine of the cube root of the natural logarithm of the hyperbolic tangent of … you get the idea.

This time you’re screwed.

Going in value order won’t work. Going in a spiral won’t work. Going in alphabetical order by the description of the number won’t work. The number may have an infinitely long description or even none at all.

The set of irrationals is an uncountable infinity — there’s no way to order them so that you hit them all. A fellow named Georg Cantor proved it in 1874.

Whatever strategy you use, you’re going to miss some numbers.

Of course, you could still get lucky. The devil could pick something simple like the square root of 2, and you could just happen to guess it. But you’re no longer guaranteed to win the game.

So … enjoy perdition. You’re going to be there for a while.

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Converting repeating decimal to fraction

10/12/2022

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The “period” of a repeating decimal begins immediately after the decimal point. Sometimes, this is referred to as the repeated block.

Write the period of the repeating decimal in the numerator of an ordinary fraction and write some number of nines in the denominator of an ordinary fraction. The number of nines must be equal to the number of digits in the period of the repeating decimal.

Take a repeating decimal 0.3 as an example. (A bar over the three is usually used to indicate the three is repeating). It has zero integers and a three in the period, the place after the decimal point.

Convert to a fraction.

The rule states that the period of a repeating decimal should be written in the numerator of an ordinary fraction. So, in the numerator we write 3.

The denominator must contain some number of nines. In this case, the number of nines must be equal to the number of digits in the period of the repeating decimal 0.3.

In the repeating decimal the period consists of one three. So, we write one nine in the denominator of the fraction: 3/9

The resulting fraction 3/9 can be reduced by 3, and then we get the following: 1/3

Thus, when one translates the repeating decimal 0.3 into an ordinary fraction, one gets 1/3.

Want to try 0.45 repeating? The answer will be 5/11.

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squares

10/11/2022

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Quora math question

In my math homework problem, they ask me to prove that a number which is made up with 12 ones and 13 zeros cannot be a perfect square. Can anybody help me prove it?

Answered by Sanket Alekar, math & geography nerd turned stand-up comedian

A number with 12 ones and 13 zeros has a sum of 12 when all the digits are added.

The number 12 is divisible by three, meaning that the long number is divisible by three. However, 12 is not divisible by nine, meaning that the long number is not divisible by nine.

If a number is divisible by three and not by nine, that means it has only one factor of three in its prime factorization.

12/3 = 4, 12 = 3x2x2 (only one 3)

As a result, it cannot be a perfect square, because in perfect squares each prime factor must appear an even number of times. E.g.: 3x3 = 9, 2x2x2x2 = 16

[answer edited slightly]

I would add, “It is helpful to think of more numbers, such as 27. It does not have an even number of prime factors: 3x3x3. Remember, a prime is divisible only by itself and one. Now, think of 36, a perfect square, which is 2x3x2x3. It has an even number of prime factors, two two’s and two three’s.”

pentecost 2033

americanisms

counting trees

parallax

involute

moon drift

gibbous

math 8

euler

bee geometry

balloon shoot down

latin mass chuckle

subterfuge

cnn vs fox

azimuth

glaciers

exponent properties

power of x

square root of -9

chess

nth root

uncountable infinity

Converting repeating decimal to fraction

squares

combinations

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