In Euclidean geometry, squaring the circle was a long-standing mathematical puzzle that was proved impossible in the 19th century. The term also has been used as a symbol in alchemy, particularly in the 17th century, and it has a metaphorical meaning: attempting anything that seems impossible. According to mathematicians"squaring the circle" means to construct for a given circle a square with the same area as the circle. The trick is to do so using only a compass and a straightedge.
The devil is in the details:. A symbol of a circle within a square within a triangle within a larger circle began to be used in the 17th century to represent alchemy and the philosopher's stone, which is the ultimate goal of alchemy. The philosopher's stone, which was sought for centuries, was an imaginary substance that alchemists believed would change any base metal into silver or gold.
Here a man is using a compass to draw a circle around a circle within a square within a triangle. Within the smaller circle are a man and a woman, the two halves of our nature that are supposedly brought together through alchemy. Philosophically and spiritually, to square the circle means to see equally in four directions—up, down, in, and out—and to be whole, complete, and free.
Circles often represent the spiritual because they are infinite—they have no end. The square is often a symbol of the material because of the number of physical things that come in fours, such as four seasons, four directions, and the four physical elements—earth, air, fire, and water, according to ancient Greek philosopher Empedocles—not to mention its solid appearance.
The union of man and woman in alchemy is a merging of spiritual and physical natures. The triangle is then a symbol of the resulting union of body, mind, and soul. In the 17th century, squaring the circle had not yet been proved impossible.
However, it was a puzzle no one had been known to solve. Alchemy was viewed very similarly: It was something few if any had ever fully completed. The fact that no one was ever able to square the circle explains its use as a metaphor, meaning to attempt to complete a seemingly impossible task, such as finding world peace. It is different from the metaphor of attempting to fit a square peg into a round hole, which implies two things are inherently incompatible.
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Email Required, but never shown. The Overflow Blog. Podcast Ben answers his first question on Stack Overflow. The Overflow Bugs vs. Featured on Meta.The CodeHS Gradebook allows you to customize what activities appear, view student programs, configure point settings, view supplemental material, remove assignments, view grades, and export your gradebook.
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Written by Meg Davis Updated over a week ago. Did this answer your question?Although many people have answered this already, I have simplified the numerical computation of the integral considerably by analyzing the parts involved. In fact this is just an elaboration of my original approach before I saw that Scythian gave an expression for the area that was very similar to what I have. Here is a short description of my setup:.
Each of these situations can be reflected in the x-axis and then rotated around 0,0 to obtain all situations. The expected area of the above situations will equal the one we seek. As Scythian stated, the area of the triangle P1P2P3 is the absolute value of.Apex legends error unknown error
But it has a very smooth graph and can be integrated numerically to a high precision using Simpson's rule:. Here is a list of the results I got applying Simpson's rule for different values of n, adding the 3.
I have used bit-precision and the decimals are truncated not rounded after 24 digits. The last one was computed in less than a minute and it appears as if the last few agree on the digits. So the analytical work did increase the precision of the figure considerably. The important thing is that we have a single variable integral now rather than a three variable triple integral disaster! I am using Sage, which has high precision, but sometimes is a bit slow.
I got:. My GeoGebra-document handled the numerical integration to 15 decimal digits in a few seconds. It only disagrees with Fred, Scythian and I on the very last digit.
Fred: Very interesting suggestion! I am not sure how you found that fit if not by LS, though? So it was more than 2 digits per second I could ask for more, if I wanted to. When I asked for just digits the result was in perfect accordance with all of Scythians digits.
First, let me point out that these sorts of problems often have a hidden trap -- in the word, "random. I like xyzzy's approach. It occurs to me that his expression for the area, given the three coordinate pairs, can be organized into a sum of 3 cross products. Well, that might be prettier, but it isn't a tremendous help. But note that we can exploit circular symmetry here, and fix the first point, say, at. It's the absolute value enclosing all that, that makes it so opaque.
Maybe that's why his and xyzzy's answers both seem about right, but clearly disagree. That allows each part of the split to be re-written without the absolute value.Traceback most recent call last : File "scratchpad.
I've been working on this for a few days, and it seems like every change I try making throws a different error, can anyone help so I can get past this? Ive been trying to understand unit 9 but I am really struggling. I am currently having trouble with 9. If someone is kind enough to help, can you DM me? Thank you so much in advance, I am on a time restraint and anything helps! I used the Mobile CSP curriculum, which was great!
With COVID in the air, chances are pretty good that we're going remote for a portion of the year, and I can't teach a curriculum that relies on students having an Android phone most have iPhone or capable computer at home. I was wondering if anyone had experience with one or both! In particular, I'm wondering.
So my code works pretty well so far as I'm coding an entire breakout game. So far, I have coded the bricks and I'm onto the paddle, but one issue I've run into is that the paddle keeps sort of multiplying when in the very edges of the restricted zones end of brick zone and walls of canvas.
Any help is seriously appreciated! Here is my code:.
If any of you want to help your girl out, send me over some answers. I am so behind and I cant get any of them. Then, let the user input letters using readLine and print whether each letter they enter is a vowel or not. If a letter is in the set, then the letter is a vowel. The last element in each array in a 2D array is incorrect. In the second array, the final value should be the sum of the first value, and the second to last value in the array.
Create a method called fixArray int array, int row, int col, int value that sets the [row][column] to the correct value. Then, call the fixArray method three times - once for each value change that you are supposed to make. When inputting values to fixArrayyou will have to hard code the row value, but the column value and the new value should be set using the array accessor methods. For example, if we wanted to set the value of the first index in the first array to the length of the 2D array, we wo.
The Strings are the message that should be printed. You should alternate between the Strings after each line. The int represents the total number of lines that should be printed.
If there is no point where the condition becomes false, you will create an infinite loop which should always be avoided! Naming Functions: You can name your functions whatever you want, but you can't have spaces in the function name. We use variables to store values that can be used to control commands in our code.
The variable values can also be altered throughout the code. Use an if statement to tell Tracy to do something only when a condition is true.Motor mounts built
If the condition is false, Tracy will skip the commands indented underneath. If the first condition is false, Tracy will skip to the next condition until she finds one that is true.
We use comments to leave notes about the code to the reader. Comments are not actually run by Python, they are just there to help us read the code. We can make multiline comments with """ and single line comments with.
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