Online Version Of P90x

[The Problem of the Week] Square squared and more

Another published in Dodka old problems, which, as usual, I lost the source and I can not say now where you extracted.

I took a number and found its square. After I have raised this square to square and multiply the result by the original number. At the end of my calculations, I find as a result a number of 7 digits finish 7. What is the original number?

The solution will not be expected, as the image let it pass.

[This image is taken from the web Grand Illusions. Consists of a simple toy consisting of six squares made of clear plastic with three colors, and joined by a corner with a piece of rubber that can be pasted to a window, for example. With the light coming through the window, the children can play to turn over to the squares and discover the different shades of colors that are formed by combining the squares together. I recommend visit grand-illusions.com Because it is full of all sorts of objects and toys magic, optical illusions, and articles and videos of many of them]

Solution:

If we square, then back to square and then multiply the original number, we are bringing to the fifth:

(x ² ) ² · x = x ⁵

We have to find a number raised to the fifth of a result seven digits ending in 7. This can be done to score, but it is sufficient to prove with numbers ending in 7, because only they can to last digit 7 as they rise to the fifth power (those ending in 3 also can give 7 in the last figure, but not when they rise to the fifth power).

After some trial and error is found that 17 ⁵ = 1419857, ie 17 is the only number it does.

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More of the same work I do not

If we sell the bike here from "This is used by the oriental medicine for thousands of years" (how old, no?), How the crap sold there type bracelet, berries, massages and various alternative energy?

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Logbook: This morning, through the dense fog, I spotted the shape of a ship known aspect and fearless spirit I asked the helmsman to put due to the strange ship. It was not difficult to sail the high sea between us, and when we have come closer to the boat we found to our surprise with the disturbing, ghostly presence of Dodka , we assumed wrecked several months.

Despite our voices and signs have not received a reply, nor have we been able to see any crew on board the ship looks abandoned to their fate. Both myself and the rest of the matemarineros dominated by superstitious feelings, we have avoided addressing the strange ship and then to accompany him for a while on his way to drift slowly apart, we have it. Finally the fog swallowed him again, and I doubt that we will find again in our journey.

I do not know if their cellars keep intact that which once contained, I think if I did not find out. Dodka Goodbye! Still plying the wide space of your travel matemares random! Be one of the legends and mysteries that populate the vastness mateoceánicas! That storm respect you, water is not your strong frames and rotting fish pass be surprised to see the sun shining skies!

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The ghost ship [The Problem of the Week] Sums of odd

Today, another of the old problems of Dodka:

We have commissioned let us add all the odd numbers from 1 to 101 inclusive. After a while We have completed the account, but then we have commissioned the sum of 1 to 201, and tired of adding, we want to find an easy formula to give us the result.

Find the formula, and as application calculates the sum of the odd numbers from 1 to 101, from 1 to 201 and from 1 to 343.

Where is the solution? Just past

illustration. Girard

wheel on your mouse;

the

find

without delay.

[This image is taken from an activity by George Hart at Albion College (Albion College ) in the summer of 2008. Shows the lobby of the university, which led Hart to various groups of people to assemble the geometric structures which were then hoisted and hung at different heights, as shown in the photo. In total there are nine shapes, even in the picture are only eight, and are positioned so that its sequence inspired by the flight of an asteroid or comet in space. Surprisingly, although the structures are perfectly regular, Hart has made an intricate shape that together with the chosen colors suggest the irregular shape and rugged incandescent rock entering the Earth's atmosphere. See note at end of this post for more details on George Hart]

Solution:

Just keep trying with the first sums of odd and realize what's happening:

1 = 1 = 1

2 1 + 3 = 4 = 2 2

1 + 3 + 5 = 9 = 3 2 ...

The sums of consecutive odd numbers always gives the square of a number, specifically the number being the odd arithmetic mean we used. If we add up all the odd numbers from 1 to 101 will leave the square of the number that is average between 1 and 101:

(1 + 101): 2 = 51, then

1 + 3 + 5 + 7 + ... + 99 + 101 = 51 = 2 2601

And in the same way:

1 + 3 + 5 + 7 + ... + 199 + 201 = 101 = 2 10201

1 + 3 + 5 + 7 + ... + 341 + 343 = 172 = 2 29584

Note: obviously, for the matenavegantes a little tanned, this problem is actually the sum arithmetic progressions, and you can use formulas to calculate these sums, but in this particular case, adding odd numbers, we found that the shortcut explained above and the formulas are not necessary, just a little care and ingenuity.

Note: George Hart page is one of the latest discoveries in our journey of matenavegación. We recommend that all school officials Ships that visit, because it is full of exciting activities. One of them, namely that Hart held at the University of Seville in October 2008, we have repeated in our own boat, and this link you can see the results.

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Nivell C

I have no say [it], I can restate [s]. Since I have the official title of bilingualism. Now I can leave my forked tongue to roam.

And I have been told that this land is customary to burn the old things on the eve of June 24. Well, I have some old books out there ...

Who Would Reroute A Washing Machine

Young conscripts in compulsory cam service, enrollment under duress, because they are suddenly forced to shoot or shoot them

recently graduated from police academy and honest cops, cops innocent office, by being obliged to establish and maintain a police state

Students and university professors, who could know who knew or was being sought and not found the tortured, murdered and dumped the body does not know where .

Students and professors who became sought shields who betrayed and killed instead atone for sins of others

Citizens

quarreling, passing by chance, or looked out, and in the crossfire battlefield or receiving a stray bullet flew because of some explosion

Journalists brave, not so brave, brave at all, that in fulfilling their missions report died or were injured by blunt force, abuse of vehicle, shot blast, even those who were captured by mistake or through trial and never came to submit their reports or their bodies alive

Abducted, family, friends and acquaintances of the hostages, anyone involved romantically with the victim of a kidnapping for ransom to finance terrorism suitable montonero

That memory, here, and once, not so short or so selective

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Ludolph van Ceulaer and strange wording (or what looks like a van to the first 35 decimals of pi)

Logbook: among the many old papers that appeared last summer when we started to do a thorough cleaning of the cabins, I get on this blog one of them brings me a nice boy image of three or four years, which, one day of those, and my proposal, submitted an essay about Ludolph van Ceulaer .

The curious life of the Ceulaer are first encountered in a textbook, in a small article a trivia section included at the end of a topic. Ludolph van Ceulaer was a German mathematician of the sixteenth and early seventeenth centuries, who emigrated to Holland for religious reasons and was appointed professor at the University of Leiden in 1600, when he was 60. The most curious, and the reason to be reminded is that he spent the last twenty years of his life calculating pi to decimal, π, and when he died had been determined with a whopping π ... 35 decimal places:

3.14159265358979323846264338327950288.

As a reminder of his exploits, the number π with thirty-five first decimal was recorded on the headstone of his grave, and in parts of Europe the number π has been called long ludolphino number (pronounced the ph as a efe: "ludolfino) .

The number π is perhaps the most famous of the math and know its history is to find a long road full of milestones by which we can get an idea of \u200b\u200bwhat they have been many aspects of arithmetic, of geometry, algebra, calculus and analysis, and how they have evolved through time. Not a story to know or understand completely in a while, but it requires patience and progressive deepening.

π's story is full of anecdotes and curious facts. We can do a minimal summary of it, and start by saying that π was known since ancient times in his definition, "the reason or ratio between the circumference of a circle to its diameter," but one thing is definite and quite another is calculated differently.

Different civilizations have different approaches to the number π, some far from their real value, other tighter, more accurate. In the Bible, the Book of Kings, was a series of instructions for building a pot, and in these instructions implicitly assumes that π is 3. The Egyptians gave a value of 3'1666 π ... and the Greeks a value of 3'125. The Chinese are very close, giving a π value of 355/113. If the division we see that π matches in the first six decimal places (see wikipedia page for details).

is said that Archimedes was the first to suggest a method or algorithm used geometric for centuries to approach the value of π. The method is very simple: it comes to making a circle of a given diameter, and calculate its length approximated by the perimeter of regular polygons. We enrolled regular polygons (polygons whose vertices are inside the circle) and circumscribed regular polygons (polygons with sides outside tangent to the circle). As we increase the number of sides of these polygons, they go looking increasingly to the circumference, and the perimeters are going closer and closer to the actual length of the circumference, that the divide between the length diameter, we will approach the number pi to the precision we want.

This method, as we said before, was in use for many centuries. But the problem is the arithmetic. Without the help of calculators, even without the support of the logs, which are not inventoried until the early seventeenth century, mathematicians of that time were faced with tedious hand calculations to get a few decimal places of π, required hours and hours of work. The Archimedes method, despite the simplicity of its approach, this method is slow, you need to be taking many-sided polygons (thousands, millions, billions of sides) to make significant progress in the calculation of the decimal digits of π. It says, for example, that to obtain the 35 digits of π, Ludolph van Ceulaer regular polygons needed to handle 2 to the 62 sides (about four and a half trillion sides trillion = one followed by eighteen zeros, 1,000. 18 = 10 ^{000.000.000.000.000} ).

From XVII century XVIII, with the progress of the calculus and mathematical analysis, began to develop more efficient methods for calculating the decimal places the number π. Newton, Leibniz, Wallis, Euler were among the mathematicians who, through study of numerical series, they found these methods of calculation.
would be in the twentieth century when the advent of computers will enable a quantum leap in the calculation of these figures. Ferguson, in 1947, with the help of a mechanical calculator, was to calculate 808 decimals of π, but just two years later, ENIAC, the first computer, was able to compute 2037 digits of π in just seventy hours. After this event and to our days, computers have been used increasingly fast and powerful, and the number of decimal places calculated has been increasing exponentially. The latter marks the established Fabrice Bellard the December 31, 2009, the day he announced he had won a total of 2.7 trillion decimal places. In this article from El País include details.
Returning to the language that I had the boy for several years, I keep a photocopy of it and I have reread. This wording has been a disconnection paradigm that sometimes occurs between apprentices and the tasks that have to do. When the vessel matenavegantes School officials will send a task, that for them is to present something, anything That is, even without the slightest sense. And that's what I had the boy, a paper written by hand, with good lyrics, and decorated with the typical method of going slightly scorching and burning the edges of the paper to look like an old parchment, but its content had no feet or head. I reproduce below, the reader should keep in mind that the intention is to write about going Ceulaer and decimal places of pi:

Al 1500s Spain was found to a "spiritual cleansing" also known as the "inquisition ". A non-Catholics, this meant imprisonment, torture generally, and / or execution. While that the English began to conquer Western Europe, forcing many to flee to the Dutch state security.

Such is the case of Cologne, which fell to Spain in 1559. As proof of identification, the wealthy classes often joined Cologne, van Keulen van Ceulaer ("akal the suffix") to his name, which literally means "Cologne."

Eventually, the names of the "van" is recognized as surnames, and so the family of the van Keulen / van Ceulaer were created.

English Inquisition "? "Cologne? "Van Keulen? "Recognition of surnames?

guess the authorship of the writing is shared between a web page in English on Cologne and an automatic translator particularly odd and unfortunate. The boy did not seem to mind the content. Simply copied it by hand (which is not without merit) and introduced him. Subsequently I have been searching the net for the source of the wording, but I have not been able to find such a combination of nonsense.
What I liked most, by far, is the translation of an Ceulaer v by van Keulen . It reminds me how well they spent reading a booklet of instructions for installing the motherboard of a computer, in the brochure, among many other outrages, the translator of the day spoke of range of motherboard, actually referring to fan, and the only thing I missed is the board imagine wearing comb, shawl, and a flower connections between chips.

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[The Problem Week] The square Mayan good luck

This problem also appeared in Dodka long time.

in a Mayan pyramid there is an engraving like that reproduce. Below it reads: "One who calculates the square surface interior, exterior knowing that measures 100 square feet, will of God for 50 years Itzamná luck Tzolkin calendar. " If you believe in the power of destiny, get to work.

"Today we also make the solution? No? Yes? Maybe? Then look below the picture if you want to know.

[One of the activities of the Mayan people was his famous ball game, in which an H-shaped field with players vying Maya solid rubber ball to try enter one of the two vertical stone rings subjects in the central walls. The ball was hit at the waist, and it seems to shoulders, elbows and knees, but without hands, feet or head. The matches could last a day and night, and not disputed as entertainment, but as a ritual, a church that represented the Maya mythology of creation]

Solution:

is very simple, Simply turn inside the box and place as shown in the accompanying drawing, and so we will see that the surface of the small square is half of the large square.

So the solution is 50 square cm .

who does not realize this clever twist, it can be solved by the Pythagorean theorem, arriving at the same solution.

Notes: In the time do not point the source of many problems that I included in Dodka, and so far, due to some repairs being made on our school boat, I can not find these sources, so now I find that I know that this problem today I got it from somewhere, but I can not say where.

math problems are like the sayings, or jokes, it is difficult to trace the real author, as many of the problems date back to books, scrolls, papyri and ancient trails, and teachers of all ages matenavegantes have been passed to the multitude of variations and adaptations to their students in math classes. If we say that a problem as we have learned from this book, most likely the author of the book is taken from another earlier book, or someone told him at the time, and that someone else received it from someone before , etc. It is very difficult to find nowadays problems original, except when they are highly specialized in different branches of mathematics novel.

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[The Problem of the week] A broken calculator

There goes the new problem

Imagine that your calculator has broken the key of "zero." The game is to appear on the screen these numbers: 250, 205, 2050, 0.025.

And what could make the following calculations? 0.025 · 205, 2050: 250.

Remember that the key of "zero" is broken.

gosh! Where is the solution? Do not panic ... Is lower after the illustrative image.

[Speaking of calculators, this strange thing with the name of Curt is in fact a mechanical calculator invented during World War II prisoner of a Nazi concentration camp, Curt Herzstark. Clearly, the Curta name comes from the name its inventor, who survived the concentration camp and perfected the design of the calculator, by pulling the market in 1948. Were considered the best hand calculators until 1970, when it began to be replaced by electronic calculators. The Curtas can add, subtract, multiply and divide, and by design were called pepper mills. You can see wikipedia page for more details and also simulator how ]

Solution:

is evident that this problem admits multiple solutions. For example, if you want to appear on the screen 250 without pressing the "zero" we can do any calculation that gives us 250 as a solution, and there are plenty of calculations in which we need not press the "zero": 249 + 1 251 to 1, 125 2, etc ...

Then I will write one of these infinite possibilities, looking for a few operations and a certain "elegance" in the choice of numbers, using mainly products and division instead of addition and subtraction:

250 = 125 • 2

205 = 41 • 5

2050 = 82 • 25

0.025 = 1: (8 ° 5)

Once we have these opportunities, just combine the two operations for asking us the problem:

0.025 · 205 = [1: (8 ° 5)] · 41 • 5

2050: 250 = (82 ° 25): (125 ° 2)

Enlargement:

Taking advantage of our solution we have used the products and quotients, the latter two operations can be simplified and get the same result with fewer steps.

0.025 · 205 = [1: (8 ° 5)] · 41 • 5, here we simplify a 5, which multiplied with another split, obtaining the same result as follows: 0.025 · 205 = 41 : 8

2050: 250 = (82 ° 25): (125 ° 2), we can simplify the 25 to 125 and 82 to 2, and the same result as follows: 2050: 250 = 41: 5

matenavegantes

When we find a problem that has many ways of being resolved, we are not satisfied with having found those solutions, but we wonder what solutions will be the shortest, most efficient, etc. Yes, we like to matenavegantes life difficult. In our case might be interesting to find out, for each of the operations, which is the minimum number of keys you have to click on our calculator to get the result.

Thus, for 250, it seems that we need at least five buttons plus clicking the "same", although that depends on the model of calculator you have.

If we make 250 = 125 ° 2 are five keys (more of the same, but from now on we will not tell), but if we do 250 = 5 ³ 2, and our calculator has a button that lifts the bucket directly, then just have to press four keys.

Similarly, 205 = 199 + 6, here are five keys to press, but the solution given above, 205 = 41 • 5, just press four.

I invite all readers to experiment with their own calculators and try to find those keys minimum numbers needed for each calculation.

Notes: This problem has been taken from the textbook publisher SM.

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remember all victims of reasoning II Futility Futility of reasoning

reason why seek to impose? Evidently because the irrationality of rationality is natural and artificial. Against danger, to battle in the war front, the reason is an instrument that should be forced, barely worked, before the horror of the disease, an entity that does not follow human logic but has a right to be, our reason is desperately seeking explanations and conclusions. A medical oncologist must appeal to his scientific system and rigid reasoning but not too complex: Cancer is not a puzzle as a defeat that is being waged between two options. What

gives us reason to the lack of hope for a patient? Finish. Finish. Kill him and save you the horror of unspeakable suffering. Morphine. Unconsciousness. Euthanasia. Psychotic disorder with dissociation from reality: this saves curiously pain.

But man is a rational being, with or without active and malignant tumors struggle to live, to remain in that region of terror and the total imbalance is survival. The reason we suggest suicide.

he who obeys the simple reason (and for good or evil individuals are able to do so unreal) understands that to stay alive in situations that violate common sense and logic is crazy, so who obey pure reason to commit a dementia.

who choose the path of reason illuminated by choosing the loss of reason, no human being will survive.

recently in my Italian hometown is being verified by an alarming number of cases of malignant tumors in young caps of around thirty, shortly before the thirty years and soon after thirty. Amazing that in Naples, that is a thousand miles south to my hometown, in the "low Italia", recorded on ten patients with malignant tumors and caps the respiratory, eight are about thirty years. And die. A spontaneously remember the scandal of the Naples garbage, thousands of tons of waste from the four corners of Italy, one thinks of the contamination of soils and groundwater flows in the presence of high mineral soil in trash hospital and industrial radioactive slag, has a cloak of being a very good reason for that eight out of ten people have developed fast and lethal cancers from exposure to carcinogens. But cancer, my dear rationalist, do not follow any human logic and rules over mankind since the dawn of your alleged evolution without once your praise has been worthy of the name, notes that the first implementation of any technological advance is the military, unless you consider it an integral part of human progress, but I know the war has nothing to do with reason and serene splendor. What was the first use of nuclear energy? the Manhattan Project, or the atomic bomb Fat Boy dropped from the Enola Gay bomber on the Japanese cities of Hiroshima and Nagasaki. What about the invention of steel? swords and spearheads, steel and bronze before, ditto.

One of the victims of cancerous spread in Italy is a girl I know, if there was a primary school friend is someone in the neighborhood that Silvina and I have frequented. Samuela called Massignan and has thirty years. Less than three months, his mother, next of kin, died. thereafter Samuela said the symptoms of a broncho, and attributing it to the bitter cold ice in the basin did not give too much importance given the broncho epidemic in the area, then consulted doctors who believed they were facing a case of tuberculosis and fluid retention in the lungs. Today

Samuela has no hope of surviving and drugged with morphine, fortunately (so to speak) suffers almost no awareness of what is happening. The utility of reason here, or just before, and if you read is illusion to think that cancer is a random atrocity, an evil that falls from the sky or up from hell and where strikes kills without mercy or humanity, is an evil inhuman fate alien monster incubated in human bodies, "let me tell dreamer / a humanity that could never defeat, mankind undertook not to fight too busy as it was in the industrial manufacture of napalm bombs or missiles boring discarded sabot armor (APFDS) containing depleted uranium pierces a tank and explodes dismembering his driver (if you in addition assumed that such is reasonable.) And if you is that to hear such well-known monsters drop the preaching of the need to utilize the time we have in our world and "enjoy what life can be" let me laugh at his folly and advise you personally say that to accurately and Samuela or other family members, or any other dying cancer victim.

Human life is composed of and afflicted by a succession of tumors that are rarely explained by mental operations of cause and effect.

Man, be partly rational luck or misfortune kept alive only thanks to its ideals, not their ideas: the ideal of continuity and the rule of life over of every calamity, the ideal time aión against chronos, the ideal of charity and piety, and the ideal of love among many others.

Silvina and I, appalled, crushed by the news, stir in search of an ideal that we inject into vitality, for the reason lead us to flee this world with the help of a knife and so find peace and quiet, things of the famous monologue in Hamlet tells us, not have any effect on those affected by tumors, but that helps us in maintaining an ideal of life, comforts the wounded unable to resolve what happened to the dead. "

Art is not "progress."

May Providence assist us.

Best wishes and until another time.

Make Up Your Own Wwe Guy

"Individuals who are like sticks of wood, burned by a point but the other is cold" (Victor Hugo)

is backward, brain activity is the can not I control and when the mind is saturated with or without a thought ... because we have the faint of invention. There

expression. The iron logic of feuding with the expression, however we must insist, always, to achieve an outcome, because the intellect is an instrument outside service is not meant virtually nothing. Vitally is inert.

must write, eat it, whether or not readers, one is the reader himself, the extra reveals no interior lighting, the watchful eye and hysterical therefore we scrutinized from a algid clarity and shows the desolation of the objects that surround us.

reasoning power fed into the mouth to the violence that we contain, we are not surprised that the most unfortunate outbursts are born of a meditative contemplation, in which case power our despair, and no way out, those who have chosen inventing things, fiction, lie, fables, fantastic.

defeat

So get a reality that we should see, but her look after us, and that there is no escape except suicide. Like

including a description of Napoleon I found a biography of Vittorio Alfieri:

"This young commander who all speak, able to bring their armies to victory in conditions that defy logic and strategy" .

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[The Problem of the Week] full, half full and empty

The problem of the week for apprentices:

Three brothers received 21 identical sealed bottles with different amounts of an orange soda: 7 were full, others 7, half-full, and the remaining 7, empty.

How divided the 21 bottles so that each receives the same number of bottles and drink the same amount of unopened bottles?

The solution, of course! Below the photo.

[In the picture you can see a three-dimensional model Klein bottle, a closed surface has no interior and exterior, and is equivalent in area closed to the Möbius strip . We, in our three dimensional reality, we are used to closed surfaces, like a soccer ball, a closed bottle, an unopened box, with interior and exterior, and can not be passed from one to another without breaking or going through the area. In reality, the Klein bottle is a three dimensional object, but four-dimensional (the fourth dimension), a surface that does not cut itself, but as shown in the picture, to represent in three dimensions is needed that " neck "of the bottle finish inside the" belly "to join the fund, through the surface, something that would not happen in four dimensions. The picture seems very nice: note the absurd scale of measurement, in which the volume content is always zero (in fact, having no inside or outside, anything that is "meta" in the bottle can not be isolated abroad, which this bottle is good for "saving" anything) also note at the bottom the English phrase Imported from the 4th Dimension, "imported from the fourth dimension." The image was taken from this site ]

Solution:

We first realize that in total there are 21 bottles, and soda are 7 whole bottles and 7 half bottles, which are 10 ½ bottles, thus spreading among the three, each must have 7 bottles, and soda 3 ½ bottles each. There are at least two different solutions, as anyone who thinks a little can be discovered, and I think they are the only two solutions.

One solution might be:

-the first brother, 3 full bottles, 1 bottle half full, and 3 empty.

, the second brother, 3 full bottles, 1 bottle half full, and 3 empty.

, the third brother, 1 bottle full, 5 half-filled bottles, and 1 empty.

A second solution could be:

-the first brother, 2 full bottles, 3 bottles half-full, and 2 empty.

, the second brother, 2 full bottles, 3 bottles half-full, and 2 empty.

, the third brother, 3 full bottles, 1 bottle half full, and 3 empty.

Note: This issue has been taken from the textbook publisher 3 º ESO SM.

Head Scissors Long Ways

Three black shirt bearing

While I hope that the author shows signs of brain activity, I would solve a internal quarrels.

Personally I have nothing against the fascists, so far could be one that would be me, but I can not say that I love. But what do we mean by fascism? State terrorism, use of the arrogance, suppression of civil rights, support of the armed forces and so on. The aura of folklore surrounding the dark stain of fascist power. We have fascism in action without a de facto government, politically we have the components in the regency supracitados any ideology, sinister word evocative of European post-fascist decade.

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Victor

Hugo Morales

It's nice to travel to Paris, all payments including hotel, it's nice stroll through New York and attend the opera house
and Continental pay. When will a trip to the Uruguay round. Hysterical, interested, sold, resentful, and bon-vivant oficilista but uncommitted

José Pablo Feinmann

There is an error: the Prestige is the cousin of Eddie Hadad pimp, although this beats all ten heads and sucked both socks since he was hired to liquidate Blumberg that he locked the neck, jaw is contorted lower callus was formed on the tongue. Chanta epitome of Argentine philosopher toilet and toilet paper edition. Know this, not all Jews are smart

Alejandro Dolina

Or only the middle class deserves to die, perhaps because he is part of the high. It is simply a phrase, and no hard feelings because you're nothing but a poor guy: matate once, miserable ...

Someone has to deal with propaganda, or intellectualization of ideology under which the regime is moving signs, intelligence-I apologize for the pun-the regime. And commended the effort they put some of its proponents to defend the indefensible, to the detriment of modesty, shame if necessary