Music and Mathematics – there are many Connections


If you thought music was not mathematical language, then think again. In fact, music and mathematics are very much intertwined, so much so that I think you might say could not live without the other. Here we explore the relationship clearly shows the strength of this tie. Let the music begin.

For those with a rudimentary knowledge of music, diatonic scale is something quite familiar. To understand why certain pairs of notes sound good together and others do not, you need to look into the points pattern wave physics and frequencies. The sine wave is one of the basic pattern surge in mathematics and is displayed well alternately Crest-lowest extent. Many physical phenomena and real-world can be explained by this basic wave pattern, including many of the fundamental tonic properties of music. Certain musical notes sound good together (musically this is called reconciliation or consonance ) due dots pattern waves strengthen each other at select intervals.

If you play the piano, then how each of the different notes sound to you depends on how your instrument is configured. There are different ways to tune instruments and these methods depend on mathematical principles. These artefacts are based on the whole frequency applied to a particular mind, and as such, this product whether groups of notes sound well together, but we say such comments are in harmony, or incompatible, but we say such remarks are out of harmony or dissonant.

When this product coming from the launch of criteria instruments manufacturer and today there are certain criteria that these fabricators follow. Still criteria Despite a multiple nature of mathematics. For example, in more advanced mathematics, students learn some numbers. A series is simply the pattern numbers are determined by some rule. One famous series is harmonic series . This includes the reciprocals of integers, it is 1/1, 1/2, 1/3, 1/4 … The harmonic series serves as one set of criteria for certain tunings, one in particular called Pythagorean intonation .

In Pythagorean intonation, comments are set according to “ rule that perfect fifth .” A perfect fifth consists of “ musical distance ” between the two tones, such as C and G. Again without trying to turn this article into a thesis on musical theory, are notes between C and GC #, D, D #, E, F, F #, and G. The “ from ” between each of these notes is called a half-step. Thus, the perfect fifth 7 half-step, CC #, C #, D, DD #, D # -E, EF, FF # and F # -G. When we consider the notes in a musical harmonic series, a number considered a C note and attributed to G mind will always be in the ratio of 2: 3 So the frequency of these notes will be adjusted to their ratios in accordance with the 2: 3 There is C- note the frequency will be 2/3 G-note frequency, or vice versa, G note frequency will be 3/2 C note frequency, the frequency is measured in cycles per second or Hertz.

Now, continue to adjust according to the perfect fifth, fifth above G is D. Use perfect fifth rate , D note will be tuned to the frequency of 3: 2 G frequency or watched from below, G note is 2/3 frequency D note. We can continue the same way until we complete what is called Ring of the fifth , bringing us back to the C note by applying a series of ratios 3/2 in the previous note in the cycle. This includes the Twelve Steps and when complete, the frequency of the second C or higher octave C note should be exactly twice frequency lower C note. This is a requirement of all octaves. But this does not happen by applying this ratio to 3/2.

Musicians have corrected this problem by resorting to none other than the field irrational number . Recall that the numbers are such that they can not give up the offense, that is, a decimal representation of them, like the number pi or the square root of two, providing not and do not repeat. Thus failure of a Pythagorean tuning method for producing perfect octaves, tuning methods have been developed to prevent this situation. Is called “ equal temperament ” Tuning, and this is standard procedure for most practical applications. Believe it or not, this tuning method involves the rational powers of the number two. That’s right: folded chose number two . So if you thought you were studying rational exponents for nothing in algebra class, here is one example of where such a debate is used in real life

Route equal temperament tuning works as follows :. Each note through its octave has a frequency multiplier repeated twelfth root of two to get to the next higher note. That is, if we start with the traditional note, which vibrates at 440 Hertz, let’s say, getting to # 440 multiplied this by 2 ^ (1/12). Because the twelfth root of two is equal to 1.05946 to five decimal places, A # was tuned to 440 * 1.05946 or 464.18 Hertz. And so continues tuning with the next Note B by taking 2 ^ (2/12) * 440. Note that with the increase of twelfth power 2 by 1 every time the power 2 of 1 / 12, 2/12, 3/12, etc.

What is nice about this process is exactness, unlike inexactness of Pythagorean intonation method discussed earlier. Thus when we arrived at the octave note, almost on top of the standard A, which should vibrate twice the original frequency of 440 Hertz A, we get A octave = 440 * 2 ^ (12/12) 440 * 2 = 880 Hertz, as it should be — exactly. As we noted earlier, when the set of the Pythagorean method, this does not happen because of repeated use rate 3/2, and the accommodation must be made to bring into line the inexactness of this approach. These great cause noticeable dissonance between certain notes in certain keys.

This tuning exercise shows that math and music are closely intertwined, and indeed it can be said that these two disciplines are inseparable. Music truly is mathematics and mathematics is well, yes music. Since many people think of musical talent coming from “ creative” species and math capabilities come from “ nerdy ” or non-creative types, this article is in some part help disabuse these same people of this idea. Yet the question is: If two ostensibly different fields like music and mathematics are happily married, how many other areas out there that at first seem to have nothing to do with mathematics, are just as intricately linked to this most fascinating material. Consider that for a while.


Math Games – the number of rows (Part 3 of 3)


In the previous two articles we looked at the types of numbers the number sequences are often used as the basis of “What comes next?” questions IQ test. In this key findings article we will look at two more types of number sequences that are used in ‘What comes next? “Questions. Geometric progressions and special or” one-off “number sequences are the least numbers progressions, but it is a different reason for this in each case. Geometric progressions are mathematically complex than numbers progressions, making only the simplest geometric number sequences suitable for use the IQ test questions. The goal IQ tests measure intelligence, based on the combination of speed and accuracy of the answers of the other party, meaning questions that require long calculation is not suitable for inclusion. However, individual rows speak rarely used in IQ tests for they tend to favor those with more extensive education and pattern recognition skills, rather than those with innate intelligence.

Geometric Number Sequences

A geometric progression is a sequence of numbers each number in the series, but the first is found by multiplying the previous one by a certain number, which is known as a common rate. The corporate rate can be either positive or negative number.

Positive Common ratios

For example, the order of 2, 8, 32, 128 … is a geometric progression with a common ratio of 4, 40, 10, 2.5, … is a geometric series with common ratio of 0.25.

To check whether the sequence of numbers is geometric, one simply checks whether the subsequent entries in the series all have the same ratio.

If the common ratio is greater than 1, the series will grow inexorably to infinity. However, the common rate between zero and 1 will produce a series of decays toward zero. A common ratio 1 produces dullest geometric series, stable series where each number in the sequence is the same example, 5, 5, 5, 5, 5, 5 …

Negative Common ratios

Negative common ratios produce alternating series, where the legs numbers change from positive to negative and back again.

For example, the sequence 1, 2, 4, -8, 16, -32 … is a geometric progression with normal rated -2.

If compared to the common rate is between zero and -1 it will produce alternating order decays toward zero. A common ratio of less than -1 leads alternating series showing exponential growth towards infinity. A common ratio of -1 produces alternating continuous series such as -5, 5, -5, 5, …

final chance to be aware of the common rate of 0, which produces a range comprising the first number and infinite series zero eg 5, 0, 0, 0, 0, 0, …

Special Number Series

Special or “one-off” series of statistical series that have mathematical basis, but recognizable by the model rather than the underlying mathematics. The best-known series, which might seem a question of IQ test, prime numbers. A key is a number that has exactly two integer share, and the number itself and 1. Series starts primes 2, 3, 5, 7, 11, 13, 17, 19, 23, …

Another, sophisticated, special series is a series of different numbers. A perfect number is a positive integer that is the sum of its proper positive Divisors. The first perfect number is 6 (the sum of its proper positive share ,, 1 + 2 + 3 = 6) and second 28 (1 + 2 + 4 + 7 + 14). In the next two numbers in the series are 496 and 8128, you will appreciate that we are entering a state of higher mathematics.

Returning to normal plane, we will do by looking at the ‘What comes next? “The question left unanswered in the second article


The problem is this question raises is that, because it seems on the surface to be in alphabetical order, many seek for an alphabetic solution. Side thinkers who consider the possibility that it is a statistical series are quickly rewarded with a correct answer. The series is the first letters of the written number sequences







make the missing letters S and E for seven and eight.

The question may seem either delightfully simple, or simply not fair, depending on whether you got the answer right or wrong. It does, however, show why train you, or your children, to perform better in the ‘what comes next’ questions should be regarded as a fun activity, rather than a sure-fire way to improve your IQ test scores.


Get Lucky Lottery Numbers með því að nota einfalda stærðfræði


Margir leikmenn segjast hafa sumir efst aðferðir um hvernig á að fá heppinn happdrætti tölur. En ef það væri sannarlega svo einfalt að vinna í lottóinu, þá hver maður þarna úti myndi fara fyrir það. Svo sem happdrætti aðferðir raunverulega vinna?

Fólk heldur að tína af handahófi tölur eða hafa það sem kallað er “fljótur velja” einhvern veginn að gefa þeim tækifæri til að vinna. Einnig, sumir myndu stöðugt standa með uppáhalds númer samsetningu þeirra. Sannleikurinn er, allar þessar aðferðir einfaldlega virka ekki, að minnsta kosti af þeim tíma. Hvers vegna? Þar sem happdrætti er ekki allt heppni. Hluti af því er byggt á líkum og stærðfræði.

Svo hvaða hjartarskinn stærðfræði að gera með heppinn happdrætti tölur? Svarið er mikið, því að happdrætti felur kenningar líkindum COMBIN aðgerð og sjálfstætt auk háð atburðum. Fyrst og fremst, kenningin um líkur er í tengslum við lögum meðaltöl og er hugmyndin að á lengri tíma, tölur dregin af nákvæmlega sama hátt er líklegt að meðaltali út á fjölda skipta sem þeir eru valdir.

Til dæmis, þegar þú flettir upp peningi, það eru 2 líklegar niðurstöður, sem eru annaðhvort höfuð eða hala. Ef þú flettir peningnum nokkrum sinnum, getur þú byrjað að sjá mynstur. Miðað við að það eru bara 2 líklegan árangur, og við fáum einhvers konar sögu síðustu niðurstöðum með að fá eitthvað eins og 18 höfuð og 12 hala, getum við gert ráð fyrir að líkurnar á að fá höfuð í eftirfarandi Flip er meira en að hafa hala. Þegar þú sækir um sömu hugmyndina að happdrætti, það er ekki mikill munur. Happdrætti hafa verið í áratugi núna, þannig að við höfum meira en nóg sögulegum vinnur að byggja númer samsetningar okkar á. Lítilsháttar munur er að fella við stigi handahófi sem er eðlislæg í öllum happdrætti.

Á hinn bóginn er Combin Hlutverk ráðstafanir sem tala af lifnaðarhættir sem ákveðin sett af tölum má vera á tilteknu happdrætti atburðarás. Til dæmis, að nýta Combin Virka getum við strax meta að í happdrætti 49 bolta, það eru 13,983,816 leiðir þróa ákveðna setja af 6 boltum og svona, líkurnar á hitting gullpottinn (ef þú kaupir einn miða) er 1 13,983,816.

Loks hafa óháðir atburðir engin áhrif á atburðum framtíðarinnar, né eru þeir fyrir áhrifum af niðurstöðum sem gerst áður. Teikningar eru tilvalin dæmi af sjálfstæðum atburðum, þar sem hvert jafntefli er aðskilin frá öðrum í vissum skilningi að tölurnar, sem valdir eru algjörlega ekkert að gera með tölurnar valdir í fyrra teikningu. Nokkrir leikmenn gera mistök að trúa að því lengur sem einkum koma af tölum eru ekki valið, mun meiri líkur á því sem sett er að vera valinn í síðari dregur.

Using Kerfi

A happdrætti kerfi er fær um að hækka líkurnar á að fá þá heppinn happdrætti tölur vegna þess að þeir bera nú flókið formúlu. Þetta er byggt á stærðfræðilegum útreikningum sem hafa verið þróaðar af fyrri verðlaunahafa sjálfir sem hafa notað eigin reynst sínum aðferðum til að vinna.


Mathematician and Poets – Two of a Kind?


“A mathematician WHO is not also something of a poet will never be a complete mathematician.” – Karl Weierstrass

C’mon a mathematician Who’s a poet! Give me a break. Is not that as compatible as a snake and a mongoose? You mean there really is some truth in the quote by Weierstrass, one of the most famous mathematician of all time, WHO is probably Responsible for the rigors of calculus? Indeed mathematics has a rhythmic structure Which, When probed, Reveals its poetic and musical beauty. And Any person who masters this discipline rightfully then shouldnt be regarded as something of a poet.

When my Spanish II professor Suggested That I go to Salamanca, Spain to study Castilian, I was pleasantly surprised. She had recommended participate in go Because of my outstanding performance in her class and Because I had shown Such intense interest in the subject. To this recommendation, I replied That I was a mathematics major WHO also loved-Besides foreign languages-the classics in literature as well as the sciences. To this, the professor replied, “So you’re a modern day renaissance man.”

Many people think That Those WHO excel in mathematics igniting to shun things like art and literature. Mathematics, They think, is too rigorous a subject, and Any WHO Embraces Such, could not Possibly have the softest emotional side to embrace Such flowery subjects like art and literature. Yet this is not true at all. Because mathematics has an inherent rhythmicity to its structure, mathematician are really quite sensitive to the Humanities like art and music. Even in the structure of poem, with its varied meters and rhyming schemes, Can be found the essence of mathematics.

Given the above considerations, a person should not feel awkward at being both matches mathematician and poet. Nor Should one feel Any wonder at how easilyNavigation math portability translates Into poetic portability: how one Can compose poems of varying length, meters, and rhyming schemes Because of a predispositions toward math. You see, this creative portability all comes naturally to the mathematically inclined person. And WHO knows how many of the world’s greatest poets were great mathematician? So parents, if your son our daughter shows a flair for poetry, bear in mind That you might have a budding mathematician on your hands. And Those That have children WHO are great at math, Who Knows? -Your Might very well have on your hands a world class poet.


Advantages mathematics


Many of us wonder about the benefits of mathematics in our childhood days. Many of us were not able to understand the benefits of mathematics beyond daily use in the calculation of simple numbers. Let us see in detail what are some of the benefits of learning math and marveled this arduous material at a young age.

The importance of mathematics is twofold, it is important in the development of science and two, it is important in our understanding of the functioning of the universe. And here and now it is important to individuals for personal development, both spiritually and in the workplace.

Math students living uniquely powerful tool to understand and change the world. These tools are reasoning, problem-solving skills and the ability to think in abstract ways. Math is important in everyday life, various industries, science and technology, medicine, economy, environment and development, and public decisions.

One should also be aware of the wide importance of mathematics and how it is advancing at a spectacular rate. Math is about patterns and structure; it is logical analysis, deduction, calculation within these patterns and structures. When patterns are often found in many different fields of science and technology, mathematics of these patterns can be used to explain and control natural happenings and situations. Mathematics has a lasting impact on our daily lives, and contributes to the wealth of the individual.

study mathematics can satisfy a variety of interests and abilities. It develops imagination. It develops in a clear and logical thinking. It is a challenge, with a variety of difficult ideas and unresolved problems, because it focuses on questions arising from complex structures. But it has also continued drive for simplicity to find the right concepts and methods to make difficult things easy, to explain why the situation will be as it is. Thus develops the range of language and insight, which then could be used to make a decisive contribution to our understanding and appreciation of the world, and our ability to find and make our way in it.

increasingly, employers are looking for graduates with strong skills in reasoning and problem solving -. just skills that are developed in mathematics and statistics degree

Let us look at some examples. The computing industry employs mathematics graduates; Indeed, many university computing courses taught mathematicians. Mathematics is used to create complex programming at the heart of all computing. Also cipher, a form of pure mathematics, applied to encode the millions of transactions that take place every hour through the internet and when we use debit or credit cards. Mathematics and computer science degree is a popular choice, and four-year degrees with the location of the industry are also available. The latter give graduates plenty of relevant experience to enhance their employability.

Mathematics led to the perfect proportions shown in Renaissance paintings. A study of astronomy in the early days of the beginning demanded the expansion of our understanding of mathematics and made possible such future the size and weight of the earth, our distance from the sun, because we revolve around it, and other discoveries that allowed us to continue in the body Our knowledge without which we would not have any of the modern wonders of our technology.

The computer itself is a machine based on the principles of mathematics, to be an invention so important as to bring economic revolution efficiency in data processing.


GED Math is hard?


If you are good with math, and GED math test is doable. If you hate math (or hate anything for that matter), you’ll have a hard time at 90 minutes GED math test.

What is the GED math test

Well for starters, the test is 90 minutes long. There are 50 questions. For half the class you can use the calculator as a test center provides. For the other half of the math test that you can not use a calculator. Forty questions are multiple choice. Ten questions have to be answered differently by using graph or perhaps the number line.

Four types of math questions

four types of math questions are number of operations, geometry, probability / statistics and algebra. Do these phrases strike a little fear in your memories of math? Relax, many college graduates felt the same way. (Strangely enough, my last year of college was Statistics. I did not enjoy it either.)

Mat GED math skills can be very important to you. Try to solve each of the four questions below to try to evaluate the (not fully) some math skills

Question -. Number of Operations

My outboard motor needs a gas: oil ratio of 50: 1 means that for every 50 shares of gas, I need 1 part of outboard motor oil. Gas tank for my outboard motor holds 6 liters and there are 128 ounces liter. I have 8 ounces outboard motor oil. How much more outboard motor oil do I need to buy?

  • 6 gallon X 128 ounces = 768 ounces
  • 768 ounces / 50 = 15.36 ounces motor oil needs
  • 15:36 ounces – 8 ounces of oil on hand = 7.36 ounces needed

Question – Geometry

The right angle triangle, if one of the corners is 70 degrees, what is the size of the third angle in degrees?

  • A triangle has three angles equal to 180 degrees (half circle). A right angle triangle has one angle equal to 90 degrees. 180 degrees – 90 minus 70 equals the third angle of 20 degrees

Question -. Probability / Statistics

You flipped a coin nine times and it came up heads nine times. In the tenth Flip, what is the probability that it will be heads?

  • No matter how many times you flip a coin, no matter how many heads you’ve got the order, which when you flip a coin is a 50/50 chance of getting heads or tails. Similar to the head 10 Flip is.5 (fifty percent)

Question -. Algebra

Solve for X in a statement. below

2x – 10 = 4 + x

  • 2x – x – 4 + 10 = x – x
  • x – 4 = 10
  • x – 10 + 10 = 4 + 10
  • x = 14

How can I study for the GED math test?

You need to assess your math skills. Mat math skills will help you determine both strong points and weak points in math skill sets phone. Then learn weak areas while maintaining the strength of strong spheres. You need a special approach to evaluate and improve, and test your math skills. You need help with GED math.

Here’s the best advice our GED math practice test help that allows you to pass the GED test.


CAHSEE Prep – Math Tips


The mathematics part of the California High School Exit Exam (CAHSEE) tests six main scope (called content strands). These areas are:

1. Number Sense

2. Data Analysis, probability and Statistics

3. Algebra Functions

4. Measurement and Geometry

5. Mathematical Reasoning

6. Algebra 1

These six areas making up the California academic content standards for grades 6 to 10. Since much of the material on the exam is different in nature it is important that students have a clear study plan when they start preparing for the math portion of the CAHSEE. Here are some simple tips study will help students maximize their learning time.

1. Learn one topic thread at a time. students should not skip around and learn the different content areas simultaneously. Instead, focus on one material strand at a time, learn that area, and then proceed to the next thread content.

2. Students should learn by solving job CAHSEE questions. This is one of the most important things that any student can do to really learn the CAHSEE. Students should not spend time reviewing the ideas in the text-book or watch the related class materials. Simply put, this is inefficient. The CAHSEE not tested every standard discussed in school and is not even to test all aspects of the standards that appear on the exam. Spend time solving practice problems ensures that students will not learn superfluous material. In addition, as students learn practice problems for more and more standards, their confidence will grow and this will improve their chances in general.

3. Make sure that the problem samples are standard-specific. Many companies that offer CAHSEE prep materials will be used questions withdrawn from the general test-bank practice material. These types of questions useless. The best sample questions will be directly tied to content specific state standard is tested especially CAHSEE.

If students follow these CAHSEE math tips that they will improve their chances of passing CAHSEE tremendously.


Easy Math Tricks


easiest mental math tricks are taught in many schools around the world, and the Internet is very conducive to the speed with which they are approaching. They are trying more because they are helping people solve what they have previously considered difficult math problems.

Studies have proven that easy tricks are very responsible for solving seemingly huge sums in record time. A spot check of some of them has revealed that acquiring the product between the number eg 345 672 and 11 may be less than six seconds. The simple trick lies in multiplying the number by ten and then adding the original number of the product. Of course, to meet such a large number triggers a negative chain reaction that would make one despise everything. It is obvious that after learning such simple tricks, people now respect the power of mental math tricks.

However, experts also direct reason for the high affinity of mathematics in what was previously non responsive people that the human brain. They are saying that in as much as easy math tricks are making things easier, the human mind is a super productive tool. This puts it in the position where it can easily process large amounts of information albeit slowly. The presence of these mathematical tricks have only served to increase the speed to get results. In other words, the brain is capable, just that it’s lazy.

The Easy Math mental tricks have found its way into the curriculum for young children. Most have been from ancient methods whose origin is East Asia. Experts also emphasize the use of the brain’s ability to process a lot of information within the shortest possible time. This, they noted, is going to develop a taste for mathematics while the brain is used. Mathematicians have maximum advantage of this ability of the brain, and the result is their being able to solve mathematical problems with minimal bare effort.


Easy mental math tricks are greatly affected many people liking math. Liking mathematics has tremendous benefits, health wise, to man. Internet is instrumental in ensuring that those who are interested are able to access the tricks, and they are also not to be limited to any age group. Speed ​​Despite these math tricks ensure that accuracy is also achieved. While some sites are charging for the provision of this information, others offer it for free. With the great number of things to choose from, learn basic ones is touted as the key to the development of others.


The history of mathematics


If you have taken the first years of the history of college course – or read through a basic history textbook – you may have noticed a small gap. It is only a thousand years or so

a long time, the history of Western culture was told like this :. About the fifth century BC, mathematics, philosophy and science developed, thanks to the work of some very smart Greeks such as Thales, Plato, Archimedes and Aristotle. Then Rome over Greece and Rome fell, it went dark for a thousand years or so. Then came the Renaissance on, and thinkers like Galilei and Johannes Kepler took up where the Greeks had in fact disappeared

Thanks to new historical research -. And wider understanding of non-Western countries and very rich spiritual culture development east of the Urals – this picture of the history of mathematics, philosophy and science is changing, slowly. But still, the teachers all too often skip over one of the most interesting stories in intellectual history – the way that mathematics and logic, including the best insights Greek logician, became the property of the Muslim countries in the long twilight period, from Rome’s fall to the Renaissance when most Europeans could no longer read Greek. Without the work of these great scholars of Muslims, math today might be very different animals. The Islamic Arab Empire, beginning in the eighth century, the world intellectual capital, and Arabic became the language learning to rival Latin. Some of the best mathematical reasoning in the world was done here.

We might as well start with Muhammad ibn Musa al-Hwarizmi (9th century), the Persian astronomer deeply learned in mathematics scholar of ancient India. From his name (in Latin form) we get the word algorithm, and from one of the titles of his algebra. It is right that he should be associated with the history of algebra – after all, his books preserved most of the ancient world knew about algebra (in addition to the brilliant his innovations), and his work helped to spread the use of Arabic numerals (the numbers we know and use day) to the West, so algebra lot more feasible. (To understand why this is important, imagine trying to do algebra problems while using Roman numerals: XIIa times XXVb equals c No, thanks ?.)

Then there is Al-Karam, as 1000AD found proof by mathematical induction – one of the basic logical maneuvers in math. Poet Omar Khayyam, writing in the twelfth century, laid the foundation for not Euclidean geometry. During this period, Muslim mathematicians invented spherical trigonometry, figured out how to use places with Arabic numerals (although decimal itself had long been invented by Hindu mathematicians), and developed cryptography, algebraic calculus, analytic geometry, among other things.

As important as any of these contributions, however, was the rescue of Aristotle’s text from obscurity by Arab scholars. For a long time in the Middle Ages, Aristotle was considered by Western intellectuals as one great thinkers of the world – but most of them had not read it. Few of his works that had survived the twin falls of Greece and Rome were available in sometimes poor or rather free handed and wrong, Latin translations, and many of his most important works were not available at all. Here and survived Greek script, but almost no one, at this point, could read Greek. (Widespread teaching Greek had to wait for the Renaissance -. Even famously learned scholars as the poet Petrarch struggled over it)

The same went seminal works as Euclid’s Elements, best known treatise on geometry. During this long period, when it was thought that these brilliantly logical works were gone forever, Islamic scholars kept their own copies of the translation. When European scholars began to travel to Spain and Sicily (then under Muslim rule) in the 12th century, these works and others were rediscovered in the West, leading to great intellectual ferment, including the theology of Thomas Aquinas – and understanding of logic that helped discipline of mathematics to survive and can thrive again in Western countries.


Being a Better Artist, scientist, mathematician, engineer, inventor, Leonardo Da Vinci


Leonardo Di Vinci, painter, sculptor, architect, musician, scientist, mathematician, engineer, inventor, anatomist, geologist, cartographer, botanist and writer, who was born and a symbol of the Italian Renaissance. He is known primarily for his paintings, among which include the famous Mona Lisa, the Last Supper, and the illustration of the Vitruvian man, which is seen as cultural elements in Europe, where coins, textbooks and bags have been built. Leonardo is more revered for his technical ingenuity, which he conceived ideas helicopter, a tank, concentrated solar power, a calculator. Leonardo had achieved so much in his life, and as a tribute to the great thinker I did some research and came up with clues that will bring us further towards how this great thinker the world.

genius Leonardo can be identified by understanding where he grew up, his experience, and also by how he digested the world around him. In this article I focus on the latter, how he digested the world around him, but the first two are obviously of paramount value to understand how he came to be. It all began in 1452, where Leonardo Da Vinci was born in Vinci Tuscan hill. Interestingly, Leonardo was not born with the name of the Lord, his name Da Vinci simply means “from Vinci,” marked by his birthplace. His father was fairly wealthy peasant and mother, and about his childhood, his father, who lived with had married four different wives. By the age of fourteen Leonardo apprenticed with the artist Andrea di clones, it was here that he was exposed to what could be labeled one of the best training in the art of Florence had to offer.

In order to understand the mind of Leonardo, we are going to take advantage theory spun psychologists and other mental health experts, the world is generally three procedures, visually, kinesthetically (with emotions) and hearing. The theory holds that people have a strength in either what is vision, what we can find, or what we can hear, and it is this strength that was a significant part of people work, personality and attitude of the events taking place around them.

“If you historians or poets or mathematicians had never seen it with your eyes and you would be ill able to describe the writings. And if you, O poet, represent the history of the show it with a pen, a painter with his brush, will then do what to be easier pleasurable and less tedious to understand “

Leonardo of his work has shown a clear preference for things that are visual. This is the first step to understand why he ended up showing art as well, way in which he saw the world. If one puts a clear specific selection of all things visual, had his time has been spent wondering visual images, drawing, painting, and illustrating. Saper Vedere (“knowing how to see”), this is what Leonardo put at the forefront of how he analyzed the structures, forms, nature and the world. For Leonardo, knowledge was simply taking an idea, a concept, and then conceptualizing it clearly pictorial way.

So how Leonardo drew so well, does not only look at the world through a visual point of view. This is an excerpt of Leonardo

“When you want to know anything well of the heart that you have studied this process: Once you have drawn the same so often that it seems that you know it by heart trying to do it without the model, but have traced from the model of a thin piece of smooth glass and lay this to draw you make without making Note well where you want to have it in mind in order. not to make mistakes again. Even the back of the model to copy the part where you were so wrong times and to fix it in your mind. “

This is a similar quote of Picasso popular in our time with Steve Jobs, to read “good artists borrow, great artists steal.” I both artists agree that to learn something one must first copy it, in fact, everything we do is based on something you have seen or experienced in the past, so every creation is based on copying before seen picture. Thus to be a great artist, or think alike to Leonardo, it is important that you allow yourself to be aware of this idea that all representations are simply the result of what we have experienced in the past. To learn something, be relentless in copy form in which it has been laid out.

If one is to learn how to speed up the tie, Leonardo suggests studying various types of facial features of heart. For example, as cited in his writings, “If you want to have a facility to keep in mind the expression of the face, first to learn by heart the various different types of heads, eyes, noses, mouths, chins, necks and also neck and shoulders … when you have to draw a face from memory, carry with you a small notebook in which you have referred to such actions, and so when you cast a glance at the face of the person you want to draw you can run privately and see who mouth or nose resembles it. “

Leonardo had thought a good time to review research on the levels to be awake and asleep. While lying in bed before you sleep, and just as you wake up are times where if you go over what you’re trying to learn, it will be easier to memorize. This is now explore the concept in psychology, there is a condition called trance, a trance unconscious learning is much easier.

Leonardo believed that in order for us to understand something we have to analyze it from different angles, cited when describing how he draws the human body, “it with my drawings every part must be known to you, and all of demonstrations from three different perspectives of each part. ” When drawing the human body, he also believed that it was necessary to take into account all factors, including the purpose of organ one draws, its beginnings, and also the status of transplant patients experience death. His drawings were not just pictures, they were too abstract map of the system that he drew.

When judging own photo Leonardo believed that it is wise to consider the human spirit, we are likely to face similar drag us that if we are ugly, we must draw a grim picture. He points out that we are less likely to see defects in our work as closely as others can, thus, he suggests looking at your work through the flat mirror, or go for a walk and then evaluate your work by relaxing. He also includes a view of the work from a distance will give a similar effect, it will allow you to see your work more so as it is, but what you want it to be. “Simplicity is the ultimate sophistication,” further promoted in today’s generation of Steve Jobs. Leonardo recognized the power of simplicity has beauty and class, it is possible to have something that is simple. Compare this with the popularity of the iPad many Microsoft products, iPad is actually a very simple device, simplicity seems market appeal.

“It is easier to resist at the beginning of the end,” first step can be difficult sometimes. When you start something new it must be admitted that in the beginning may greatest reluctance. And when working on a project it is advisable to follow your experience, not your mind, that “each device needs to be experienced.”

Last lesson I will present what I had learned by reading the works of Leonardo, was his desire to create something special, as cited “I wish to work miracles . ” The desire to create content from the ceiling was written about his work, in which he compares himself to Alchemist on more than one occasion.

In short, see Leonardo Da Vinci in the world can be better understood if one decides to take time and focus on the beauty of all that is visual, if you take your time to understand the purpose of things that you see . If you appreciate the idea to learn something you have to copy it to where it can be done without a guide, and the best time to learn something new is in the state of trance, just before bedtime or just when you wake up. When learning or detect something that’s extremely important to take multiple perspectives, and the desire to achieve the miracle is also necessary mix to level. Keep in mind the simplicity of the product once it has been completed, as it is the ultimate form of sophistication. Walk around with your laptop and keep in mind the importance of experience to the job, and the first resistance that may arise when pursuing new projects.