Who is he? Leonardo of Pisa, mathematician, circa 1170-1240-50. In 1202 he developed a sequence that began as a solution to a problem involving mating rabbits: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, etcetera. The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding numbers. When we make squares with those widths, we get a spiral:
courtesy of mathisfun.com
The counting numbers are written out as one long string: 123456789101112 … What is the 100th digit in the string? Show how you solved it! Show your work.
William Graham, B. Sc., Computer Science, University of Calgary, answered today on Quora.
First, he solved with Python script, and then he said, “It’s easily verified by splitting the string into lines of 10 digits each, and looking at the tenth digit of the tenth line.”
The answer is 5.
If the Earth rotates with 1600 km/h and planes fly at 600-700 km/h, how do they manage to fly eastwards?
Robert Frost, Quora contributor, Instructor and Flight Controller at NASA, answered the question on Feb 2, 2020, first by quoting Sir Isaac Newton’s First Law of Motion: “An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.”
My conclusion: force would be the jet engine.
The prime minister of Spain is an outspoken atheist and socialist. The prime minister of Canada might as well be one, too. The US president and the governor of California make three and four. They are the apathostics. All you do is add up.
“… when the struggle seems to be drifting definitely towards a world social democracy, there may still be very great delays and disappointments before it becomes an efficient and beneficent world system. Countless people … will hate the new world order, be rendered unhappy by the frustration of their passions and ambitions through its advent and will die protesting against it. When we attempt to evaluate its promise, we have to bear in mind the distress of a generation or so of malcontents, many of them quite gallant and graceful-looking people.” Quote from The New World Order, by H.G. Wells, 1940, courtesy of Wikipedia.com.
Wikipedia calls the New World Order a conspiracy theory, but Wells might have seen the coming future. He was a science fiction writer. Would he think I was a gallant and graceful-looking person? Yes, I think so because I can add up. You can be one, too, with this math trick.
From Tom Schulenburg, Quora contributor, 12-16-21
Why is the shape of an elephant related to Fibonacci numbers?
Starting with 1, 2, etcetera, the Fibonacci sequence is derived from adding the two previous terms to create the next term - (1+2) = 3, (2+3) = 5, (3+5) = 8, and so on.
As the sequence progresses, the ratio of two terms (term2/term1) becomes consistent at about 1.618034. This is known as the golden ratio. As nature would have it, this is a ratio that appears frequently in many forms - the spiral of a snail shell, the petals on a flower, the shape of a hurricane, to name a few.
The same ratio can be seen in the elephant’s trunk when curled up.
The nth term of a sequence is 7n – 5. What is the 86th term in the sequence?
All you need to do is put 86 in the place of n in your formula.
So, the 86th term is 7 × 86 – 5 = 602 − 5 = 597.
What does (−2)² mean?
Answered by a seventeen-year-old boy on Quora: 4. One thing to note, (−2)² is not the same as −2². We can write −2² as −(2²) which becomes −(4) = −4.
When the priest said today that chances of conversion are not endless, his words got me thinking about math. When you roll just one die, there are six different ways the die can land [six chances]. When two dice are rolled, there are now 36 different and unique ways the dice can come up [36 chances]. This figure is arrived at by multiplying the number of ways the first die can come up (six) by the number of ways the second die can come up (six). 6 x 6 = 36. [courtesy of Ed Collins, edcollins.com] What if, instead, there is concomitance, the fact of occurring together? With one roll, we could get two three’s. Consider what the Missal says …
Body and blood are separated at death. The crucifixion empties the body of its blood. The priest separately consecrates the bread and wine, the two species that will become the body and blood. The concomitance, or fact of occurring together, is accomplished by putting a particle of the consecrated bread into the chalice of consecrated wine. Of course, God is three in one, and, in that sense, we get two three’s because of concomitance, and that is math theology!
When near this blog, be careful how you tread,
For there’s a lot of quicksand in my head.
Here is a good teacher's solution to simplifying a square root sign under a square root sign. The solution gets rid of a square root under a square root.
Quora is an amazing community of educators. I joined Oct 2019, two years ago. My entries and comments on English and math and a little bit on other subjects have passed the 10,000 mark in terms of views. Hard to believe. Well, learners are allowed to contribute. This learner has blogged entries from Quora experts and used their answers in lesson plans. One contributor to science received 2,429 upvotes on a single post; so, my milestone is not remarkable.
There is a six chamber gun with two bullets next to each other. The trigger is pulled and it doesn't fire. What are the odds of it firing and being killed if the trigger is pulled again? [I slightly edited the question and shortened a lengthy mathematical analysis of the revolver by Jerry Liu on Quora, a Software Engineering Intern at Google 2020-present. Hopefully, I kept what is essential. SFPD officers now use a pistol, not a revolver. The edited version follows.]
When the trigger is pulled, chambers rotate, the chamber right beside the current one is moved into the trigger position, and the gun will continuously cycle between the 6 chambers.
Now … if we’re considering the chance of dying, or a bullet firing after the trigger is pulled twice … in words, this means that the gun is triggered. If it fires, it doesn’t need to be triggered again. If it doesn’t fire, then it will be triggered a second time. As most agree, the first trigger has a 1/3 or 33.33% chance of firing. We then need to figure in the percentage of the second trigger firing if the first trigger doesn’t fire.
The key is that this means one of the bullets cannot be fired without the other being fired first. The short answer is that the odds of it firing on the second trigger pull is 25%. [Jerry gave more explanation, but I left this part out.]
The chance of the first trigger not firing is 2/3 or 66.66%. Now that we have this percentage, we can calculate the percentage the same way as my original approach, obtaining 1/4 or 25%. [see above]
Since these events are tied in sequence, their probabilities need to be multiplied together or 1/4 x 2/3, which is equal to 1/6. This is then added to the 1/3 chance from the first trigger. 1/3 + 1/6 = 2/6 + 1/6, giving a final answer of 3/6 or a 50% chance of being killed. Wow, it is 50-50...anyway.
Altan (13) is learning about probabilities, permutations, and combinations. Should I give him this problem? Many people in my neck of the woods own a gun or rifle.
Ever hear of a mansard roof? There is a house with a mansard roof in Pretty City Murder. The railing on the eighth roof is a widow’s walk. No lady is made a widow in the novel. Did I give something away? I see triangles, squares, rectangles, trapezoids, circles, half-octagons, and parabolas.
The way to find the root of a variable or number that is raised to a power is to divide the power by the root. Here are some examples:
St Ouen, Rouen, France, [St. Owen] begun 1318 and rebuilt.
Public Domain, https://commons.wikimedia.org/w/index.php?curid=289116
The sum of all natural [positive whole] numbers 1 to 100 can be calculated using the formula, S = n/2 × [2a + (n − 1) × d], where n is the total number of natural numbers from 1 to 100, d is the difference between the two consecutive terms, and a is the first term. There are a total of 100 natural numbers, so n = 100.
Thus, a = 1, d = 1, and n = 100.
Let's calculate the sum of the natural numbers 1 to 100.
Use the formula.
S = n/2 × [2a + (n − 1) × d]
S = 100/2 × [2 + (100 – 1) × 1]
S = 50 × [2 + 99]
S = 5050
Isn’t that answer interesting?
Notable Catholic priests:
Here is a secular piece, so don't get into a tizzy. Some of us Catholics are capable of understanding and doing the secular as well as the sacred, so adjust your opinion.
It is an orchestral work by Vivaldi that has been transcribed for organ with a few subtitles added to explain the wintry tableau Vivaldi tried to create. As with any good story, there is a beginning, middle, and ending, and the theme is stated at the end of the beginning section, just as it is done in a good essay, but the master saves the excitement until the end. It is such a good story, you won't want it to end. I think this is the way Vivaldi and Mozart prayed. God put so much inside them that they had to let it out.
I tutor a 7-year-old genius, and he has so much inside his head, he has to get it out. He will if it is God's will. He is extremely sensitive, which is to be encouraged to the fullest. Public school tried to curb him, and thanks be to God, he was able to start homeschooling. I am grateful to participate in his education. It is an understatement to say that I admire his genius. It is rapturous.
This church in Spain is graced by geometry and fine acoustics, the application of which is present in many aspects of modern society, such as the audio and noise control industries. The plaque on the organ reads Me fecit Gerhard Grenzing - I, Gerhard Grenzing, made this organ. See the figures holding up the organ. 10 mins
Altan (13-year-old whiz) and I learned today:
1) The square root of an exponent is ½ of the exponent.
2) When you want two probabilities to occur (probabilities are ratios, such as 1:5 or one out of five or 1/5), multiply the two fractions, such as 1/5 times 1/4.
3) The square root of a negative number is plus or minus, the square root of the negative number as a positive number, paired with i, the notation for an imaginary number. √-25 = ±5i In math the symbol for √−1 is i for imaginary.
I can only describe my students’ work as operose [AHP-ə-rohs]. Etymology: Latin from opus, meaning work. In English it means displaying much industry or effort. On Sunday, 9-26-21, Altan (13) and I had a bet. “Can you figure out the next two terms in the sequence 0, 2, 8, and 18?” His answer 32 and 50. He won the bet.
A lenticular cloud is a stationary cloud formed at high altitudes. It is usually aligned at a right angle to the direction of the wind. Pilots avoid lenticular clouds because the waves of air forming them can make for a bumpy ride. On May 25, 2021, Jessica Flores, Engagement Reporter for the San Francisco Chronicle, wrote, “To learn more about altocumulus standing lenticular clouds, visit the NWS [National Weather Service] page here https://www.weather.gov/.”
Catholicism is a war with yourself, not with your neighbor. I need to osculate him or her more often. Osculate: in math, to touch another curve or surface so as to have a common tangent at the point of contact. Kiss.
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Remember, a ratio is a fraction. Opposite are two segments, labeled a and b. The equation shows how the golden ratio works.
The golden ratio is approximately equal to 1.618 and is symbolized by the Greek letter phi as shown above. The number appears many times in geometry, art, and architecture: the Parthenon shows signs of the golden ratio. The number even shows up in describing the perfectly proportioned human body and face.
A q and some d's. Quotient comes from Latin and means “how many times.” That makes sense. If one divides a number by another number, one is figuring out how many times the second number goes into the first. When dividing 10 (the dividend) by two (the divisor), the quotient is five. There are 32 ways to say divide in Latin. Here is one - divido - I divide.