A standard theorem of vector analysis due to Helmholtz states that every vector field Thus the preceding Helmholtz theorem can be viewed as a theorem about .
In view of the Helmholtz theorem of vector calculus, the surface electric current induced on a conducting body is decomposed into lamellar and solenoidal parts. The Helmholtz Decomposition Theorem, or the fundamental theorem of vector calculus, states that any well-behaved vector field can be decomposed into the A standard theorem of vector analysis due to Helmholtz states that every vector field Thus the preceding Helmholtz theorem can be viewed as a theorem about . Helmholtz's theorem states that a vector field is determined to within an additive constant if both its divergence and curl are specified everywhere . Instead of Helmholtz decomposition theorem for vector elds is usually presented with too strong Key words: Helmholtz theorem, vector eld, electromagnetic radiation. Nov 2, 2018 Helmholtz theorem. Vector and Scalar Potentials.
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Then F(r) can be uniquely ex-pressed in terms of the negative gradient of a scalar potential φ(r) and the There is a mathematical theorem which sums this up. It is called Helmholtz's theorem after the German polymath Hermann Ludwig Ferdinand von Helmholtz. Let us start with scalar fields. Field equations are a type of differential equation: i.e., they deal with the infinitesimal differences in quantities between neighbouring points. Helmholtz's first theorem: The strength of a vortex filament is constant along its length.
av R av Platon — 4Helmholtz Center Berlin, D-14109 Berlin, Tyskland 5Institutionen för matematik och datavetenskap, Freie Universität Berlin, D-14195 Berlin,
Linjära partiella differentialekvationer. Variabelseparation.
Helmholtz teorem, divergens- och rotationskällor, skalär potential och vektor potential. Gauss lag och Ampères lag på integralform. Fält från symmetriska källor.
78-84, 1985. Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1084, 2000. Problem 1. The Helmholtz theorem at last!
According to the Helmholtz theorem, the conjugate variables of A and α are found as time averages of certain functions of population x(t) and y(t). Analysis on those novel ‘state variables’ demonstrates the tendency of change in mean ecological quantities such as population range or ecological activeness when the parameter α or energy H varies. We've got 0 rhyming words for Helmholtz-Thévenin-Theorem » What rhymes with Helmholtz-Thévenin-Theorem? This page is about the various possible words that rhymes or sounds like Helmholtz-Thévenin-Theorem.Use it for writing poetry, composing lyrics for your song or coming up with rap verses.
Varfor forandras klimatet
Helmholtz's third theorem In the absence of rotational external forces, a fluid that is initially irrotational remains irrotational. Helmholtz's theorems apply to inviscid flows. Helmholtz's second theorem A vortex filament cannot end in a fluid; it must extend to the boundaries of the fluid or form a closed path.
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In physics and mathematics, in the area of vector calculus, Helmholtz's theorem, also known as the fundamental theorem of vector calculus, states that any sufficiently smooth, rapidly decaying vector field in three dimensions can be resolved into the sum of an irrotational (curl-free) vector field and a solenoidal (divergence-free) vector field; this is known as the Helmholtz decomposition or Helmholtz representation.
(du vet hans teorem) de första akustiska experimenten i världen. Vector calculus in curvilinear coordinates; Appendix B. The Helmholtz theorem; Appendix C. Units; Index. Helmholtz theorem.- Conservation of R on large scales and for adiabatic perturbations.- Spherical harmonics.- Method of Green's functions.- Polarisation. I följd af teorem C svarar alltid mot talen ö v a v ] v=0, 1,2,..
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kallas Helmholtz-rörelse efter sin upptäckare, Hermann von Helmholtz. I forbigående kan nämnas ett praktiskt teorem, tillskrivet matematikern Stokes, som gör
Vågekvationen, plana vågor, reflexion, refraktion.


Practice: Area of trapezoids. Area of kites. Finding area by rearranging parts. Area of composite shapes. Practice: Area of composite shapes. Practice: Area challenge. Next lesson. Current timeTotal duration CCSS Math: 6. Google Classroom Facebook Twitter. Video transcript What is the area of this figure? And this figure right over here is sometimes called a kite for obvious reasons.
If you tied some string here, you might want to fly it at the beach. And another way to think about what a kite is, it's a quadrilateral that is symmetric around a diagonal.
So this right over here is the diagonal of this quadrilateral. And it's symmetric around it. This top part and this bottom part are mirror images. And to think about how we might find the area of it given that we've been given essentially the width of this kite, and we've also been given the height of this kite, or if you view this as a sideways kite, you could view this is the height and that the eight centimeters as the width. Given that we've got those dimensions, how can we actually figure out its area?
So to do that, let me actually copy and paste half of the kite. So this is the bottom half of the kite. And then let's take the top half of the kite and split it up into sections.
So I have this little red section here. I have this red section here. And actually, I'm going to try to color the actual lines here so that we can keep track of those as well. So I'll make this line green and I'll make this line purple. So imagine taking this little triangle right over here-- and actually, let me do this one too in blue.
So this one over here is blue. You get the picture. Let me try to color it in at least reasonably. So I'll color it in. And then I could make this segment right over here, I'm going to make orange. So let's start focusing on this red triangle here. Imagine flipping it over and then moving it down here. So what would it look like? Well then the green side is going to now be over here.A kite is a four-sided shape with straight sides that has two pairs of sides.
Each pair of adjacent sides are equal in length. A square is also considered a kite. Each triangle has a height of. Express the area of the shape in terms of. The shape being described is a rhombus with side lengths 1.
Advanced Geometry : How to find the area of a kite
Since they are equilateral triangles connected by one side, that side becomes the lesser diagonal, so. The greater diagonal is twice the height of the equaliteral triangles. The area of the kite is given below. The FOIL method will need to be used to simplify the binomial. What is the area? Find the area. We are given the length of these diagonals in the problem, so we can substitute them into the formula and solve for the area:.
Express the kite's area in simplified form. If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.
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Area of a Kite
The kites we're referring to probably aren't the ones that David Tomlinson was singing about. Oh well. We already know that a kite is defined as a quadrilateral that has two adjacent pairs of congruent sides. If all four sides of a kite are congruent, then we just have a rhombus. That's all good and fine, but it doesn't seem like any of that will help us find the area.
But wait. If we can use the diagonals of a rhombus to find the area, can we do the same with kites? If the two diagonals of a kite are perpendicular to each other which they arethen we should be able to use the same type of formula. Let's take a look at this logically for a second. We can split the vertical diagonal into two sections as well, but we don't know exactly what ratio.
Since the area of the kite is the area of the four triangles combined, we can just add up the areas of the individual triangles. That means our final area formula for a kite ends up being relatively simple. She requests the diamond be a perfect cut, with diagonals of 3 mm and 5 mm. What is the area of the diamond's cross-section? All we need to do is apply the formula for the area of a kite.
We have the two diagonals, and that's all we need, right?
One diagonal of a kite is three times as long as the other. The shorter diagonal splits the longer one so that two isosceles right triangles are formed. If the area of the kite is Welp, we know that we have to use the area formula, but we should relate the two diagonals to each other first. If d 1 is a certain length xthen d 2 is three times that length, 3 x. Plugging in these values to the area formula should give us the lengths of the diagonals.Familiarize students with another member of the quadrilateral family and escalate practice with these area of kites worksheets for grade 6, grade 7 and grade 8.
Based on the common core curriculum, these printable worksheets emphasize calculating the area of a kite using the formula with dimensions offered as integers, decimals and fractions, unit conversions and finding the missing parameters. Type 1 offers geometric representations while Type 2 includes problems in word format too. Get into gear with our free worksheets!
Area of a Kite Integers - Type 1. Find the Area of a Kite Integers - Type 2. Bolster practice with these area of a kite worksheets offering problems as figures and in word format with two levels. The diagonal lengths are given as integers, multiply them and divide by 2 to find the area.
Area of a kite Decimals. Find the product of the lengths of the two diagonals presented as decimals, half it, round the answer to 2 decimal places to solve for the area of the kites in these printable area of kite worksheets.
Area of a kite Fractions. Plug the diagonal lengths offered as fractions into the area formula to determine the area of the kites. Area of a Kite Unit Conversions. This set of unit conversion worksheets for 7th grade and 8th grade students specifies the lengths of the diagonals in varied units.
Convert the unit as per the requirement and apply the formula to find the area of the kite. Finding the diagonal of a kite. Featured here are problems that provide the area of the kite and the length of one diagonal. Assign the values in the formula to solve for the missing diagonal. The pdf worksheets cater to the learning needs of middle school students.
Members have exclusive facilities to download an individual worksheet, or an entire level. Login Become a Member. Select the Measurement Units U. Customary Units Metric Units. Two levels of difficulty with 5 worksheets each Download the set 10 Worksheets. Find the Area of a Kite Integers - Type 2 Bolster practice with these area of a kite worksheets offering problems as figures and in word format with two levels. Area of a kite Decimals Find the product of the lengths of the two diagonals presented as decimals, half it, round the answer to 2 decimal places to solve for the area of the kites in these printable area of kite worksheets.
Two different types with 5 worksheets each Download the set 10 Worksheets. Area of a kite Fractions Plug the diagonal lengths offered as fractions into the area formula to determine the area of the kites. Area of a Kite Unit Conversions This set of unit conversion worksheets for 7th grade and 8th grade students specifies the lengths of the diagonals in varied units.
Finding the diagonal of a kite Featured here are problems that provide the area of the kite and the length of one diagonal. Type: Integers, Decimals 5 worksheets each Download the set 10 Worksheets. What's New? Follow us. Not a Member?Although a rhombus is a type of parallelogramwhereas a kite is not, they are similar in that their sides have important properties. Recall that all four sides of a rhombus are congruent.
Kites, on the other hand, have exactly two pairs of consecutive sides that are congruent. This characteristic of kites does not allow for both pairs of opposite sides to be parallel. Let's look at the image below to examine the properties that make these figures distinguishable. Despite how different they are, when it comes to areawe will see that rhombuses and parallelograms are quite similar.
The areas of rhombuses and kites are equal to one half the product of their diagonals. Mathematically, we express this as.Kites, Basic Introduction, Geometry
Recall that every quadrilateral has exactly two diagonals. This is because diagonals are line segments which connect vertices to each other.
Since there already exist line segments which connect one vertex to two other vertices in a quadrilateral, the only other line segment to draw is to the vertex diagonal from the chosen vertex.
Let's work on the following exercises, to help us apply the area formula for rhombuses and kites. The only two parts of the rhombus we need to figure out are the diagonals because that is all that is required when we find the areas of rhombuses. We are given the length of one diagonal of rhombus PQRSwhich will be our d 1.
How to Calculate the Area of a Kite
The length of diagonal PR is 12 centimeters. Before we can find the area of rhombus PQRSwe need to find the length of d 2. We see that the length of SQis just the sum of two smaller segments. However, we do not know what the length of TQ is, so we must rely on our knowledge of rhombuses to help us out at this point.
We know that the diagonals of a rhombus bisect each other. This means that the point T is the midpoint of segment SQ. Thus, we know that the length of segment TQ is equal to the length of segment ST ; they are both 4 centimeters long.
Now, we can find the length of SQwhich is our d 2 :. So, we know that d 2 has a length of 8 centimeters. Now, we have all the requirements we need in order to solve for the area of rhombus PQRS.
Let's plug our values of d 1 and d 2 in:. We see that rhombus PQRS has an area of 48 square centimeters. Find the value of y given that the area of kite YDOC is square feet. In this exercise, we will not be solving for area, since it has already been given to us.If you are looking for the formula for kite area or perimeter, you're in the right place: the kite area calculator is here to help you.
Whether you know the length of the diagonals or two unequal side lengths and the angle between, you can quickly calculate the area of a kite. For kite perimeter all you need to do is entering two kite sides. But if you are still wondering how to find the area of a kite, keep scrolling! If it's not a kite area you are looking for, check our kiteboarding calculatorwhich can help with the choice of the proper kite size for you. Kite is a quadrilateral with two pairs of equal-length sides, adjacent to each other.
Kite is a symmetric shape and its diagonals are perpendicular. There are two basic kite area formulas, which can be used depending on which information you have:. If you know two non-congruent side lengths and the size of the angle between those two sides, use the formula:. Did you notice that it's a doubled formula for the triangle areaknowing side-angle-side? Yes, that's right! Kite is a symmetric quadrilateral and can be treated as two congruent triangles that are mirror images of each other.
To calculate the kite perimeter, you need to know two unequal sides. Then, the formula is obvious:. You can't calculate the perimeter knowing only the diagonals - we know that one is a perpendicular bisector of the other diagonal, but we don't know where is the intersection. Let's imagine we want to make a simple, traditional kite. And if we're going to make an edging from a ribbon, what length is required?
The answer is almost always no. It's working the other way round - every rhombus is a kite. Only if all four sides of a kite have the same length, it must be a rhombus - or even a square, if additionally all the angles are right.During these challenging times, we guarantee we will work tirelessly to support you.
We will continue to give you accurate and timely information throughout the crisis, and we will deliver on our mission — to help everyone in the world learn how to do anything — no matter what. Thank you to our community and to all of our readers who are working to aid others in this time of crisis, and to all of those who are making personal sacrifices for the good of their communities. We will get through this together.
Updated: September 25, References. A kite is a type of a quadrilateral that has two pairs of equal, adjacent sides. If you know the length of the diagonals, you can find the area through simple algebra. You can also use trigonometry to find the area, if you know the side and angle measurements of the figure. To find the area of a kite using the 2 diagonals, measure the length of the diagonals.
Label these 2 lines x and y. Multiply the lengths of x and y, then divide the result by 2 to get the area of the kite. If you have the area and the lengths of 2 sides, multiply the length of side a times the length of side b, then multiply that by the sin of the angle, or C. To learn how to use the angle of the kite to find the length of a missing diagonal, read on! Did this summary help you? Yes No. Log in Facebook Loading Google Loading Civic Loading No account yet?
Together, they cited information from 7 references. Learn more Using the Area to Find a Missing Diagonal. Things You'll Need. Related Articles.


Once upon a time, a misanthropic teenager named Isaac Newton decided to be a genius.
The genius decided that he’d be interested in the physical properties and relations between stuff, and he’d try and describe it using mathematics. It was a wild success, and he became the father of physics or whatever.
Same guy decided to turn, like, 21 or something, and invent differential calculus for some odd reason (to describe planetary motion, I believe). Strange guy, I guess there was less light pollution back then. I’m hardly conscious of the planet’s existences up in the sky. At best, I see Venus or whatever standing out like a drama queen.
So Newton was a cool guy, among the many things he churned out was the concept of Forces in dynamical systems.
A quick run through of Kinetics – you can describe a physical system in terms of its physical coordinates. Here comes the SUVAT Equations to save the day.
When it comes to forces though, you enter the realm of Dynamics, and you encounter Newton’s III Laws:
- In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force – incoming the concepts of Inertia, and Inertial Frames of Reference.
- In an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma.
- When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.
Forces are Vector quantities, so they have both direction and magnitude tied to them. For instance, you can imagine your own weight (a force) as an arrow (a common representation of a vector) pointing straight down, whose length is the magnitude of your weight. A 200lb man will have an arrow twice as long as the 100lb girl, and so on, but that direction will always be pointing to the center of the Earth (or wherever the center of mass of the Earth happens to be).
Formally, the force applied to an object is defined as being equivalent to the change in the object’s Momentum with respect to time:
The m there is the mass of the object – but Newton didn’t quite think of it that way. Actually, that was just his lil physics-maths Constant of Proportionality, because as far as I know, all Isaac knew at the time was that forces accelerated bodies, and conversely, that accelerated bodies were acted upon by forces. That’s it.
Newton thought of that lil m as something called Inertia, an object’s ability to resist change in momentum (refer to N.Law #3). Something with a large inertia (say, a car) acted upon by a force F would accelerate less than an object of small inertia (say, a speck of dust). Obviously that dust speck will go flying with a gust of wind, but it’d take a tornado or something to do the same to the car.
It was later then, that I think inertia was tied to an object’s Mass. Of course, it makes sense now, but whatever, history lesson over.
This all comes in handy when you’re trying to pass physics exams, and also if/when you decide to be an engineer, because it describes the world pretty gd well.
Newton used the idea of forces to describe a number of phenomena in his Principia Mathematica, and one example he gave in that text was his Universal Law of Gravitation:
Which does a pretty gd good job of describing the force of Gravity.
Philosophical aside here: why does gravity follow an Inverse Square Law? I’mma look this up, see what I dig up, and update this post with a brief later. For a more “derivational”, more “grassroots” post, go check out the Universal Law of Gravitation, it’ll probs be more explicit (parents be advised, too much physics at a young age may result in social exclusion).
— Ah, it’s because we assume the effects of gravity is evenly radiated outwards, and the surface area of a sphere is proportional to the radius squared (). So if you imagine the “intensity” at a distance r from the “source”, it drops off inversely to the radius squared.


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We are very familiar with the term “(MB/Mb)ps”. It is used to measure the Internet connection speed. Actually it is the data rate unit. Data transfer rate is the average number of bits or data blocks per unit time passing through a communication link in a data transmission system.
Now when we write the term in English, the confusion arises, since it can be written as MBps or Mbps. Both the terms are different and meaningful too.
1) MBps and Mbps :
Here the two terms are different by the letter ‘B’ or ‘b’. They have different meanings also.
MBps => Mega Byte Per Second
Mbps => Mega Bit Per Second
Therefore, we can conclude,
‘B’ represents BYTE and ‘b’ represents BIT
2) Relation between Byte and Bit :
Bit = 0 or 1
Byte = 8 bits
Then, 1B (Byte) =8b (bit)
Now, 1 MBps = 8 Mbps
3) Multiples of bit
3.1) Decimal Multiple of bits
The decimal multiples of bit are, kilobit (Kb), Megabit (Mb) , Gigabit (Gb) , etc
1 kb = 1^3 bits = (1000÷8) Bytes = 125 bytes
1Mb = 10^6 bits = 125×10^3 Bytes
1Gb = 10^9 bits = 125×10^6 Bytes
3.2) Binary multiple of bit
The binary multiples of bit is kibibit (kibit), Mebibit (Mibit), Gibibit (Gibit) etc
1kibit = 1024 bits = (1024÷8) bytes = 128 bytes
1Mibit = 1024^2 bits = 128×1024 bytes
1 Gibit = 1024^3 bits = 128×1024^2 bytes
4) Multiples of Byte
4.1) Decimal multiples of byte
Decimal multiples of byte are kilobyte (kB), Megabyte (MB), Gigabyte (GB) etc
1kB = 10^3 Bytes = 8×10^3 bits = 8 kb
1MB = 10^6 Bytes =8×10^6 bits = 8Mb
1GB = 10^9 Bytes =8×10^9 bits = 8Gb
4.2) Binary multiples of Bytes
Binary multiples of Byte are
kibibyte (kiB), Mebibyte (MiB), Gibibyte (GiB) etc
1kiB = 1024 B = 1024×8 b = 8 kib
1MiB = 1024^2 B = 1024^2×8 = 8 Mib
1GiB = 1024^3 B = 1024^3×8 = 8Gib
5) Bits (b) and Bytes (B) rate
bit/s and Byte/s are common data rate units. Similarly Mbps and MBps both can be used for measuring the rate of data transferring.
Networks only worry about single transmission of bit only but hard disc or devices require full bytes (i.e., 8 bits at once) to make a sense data. Bytes are group of 8 bits. Network doesn’t care if they are grouped together in six or eight or ten or two. It transmit single bit only. Here smallest unit is a single bit.
Chip or hard drives can read bytes at a time and can’t separate bits.
So, fundamental addressable storage unit in computer can’t directly access a storage unit smaller than byte. If we want to separate or know about specific bit in a byte, we have to do an additional operation to isolate them. So here smallest unit is byte.
Since network can read bits, so data rate of computer network ( download or upload speed) is measured in bps or kbps or Mbps etc
Bytes are also used for file size, or the amount of data transferred by one device to another ( as MB, GB, or MBps, etc)
If we download a file from Internet or transfer data from one device to another then our connection speed is megabit/s (Mbps) but we are downloading or transferring megabytes (MB)
When we download or transfer a file, the file is of certain MB (megabyte) (say 2 MB) and if the transferring or downloading speed be 2Mbps ( its megabit per second), so it take 8 sec to download or transfer the file (not 1 sec)
Similarly, 1 Mbps Internet speed can’t download 1 MB file in 1 sec, since, 1 Mbps = 1/8 MBps, it takes 8 sec.
Similarly, 16 Mbps plan allows us to download maximum 2 MB file in 1sec.
Many people suspect that, thus is just people being tricked by ISP’s by using the unit Mbps since it sounds eight times bigger than the MBps
But, this unit is being used from 1970 by Institute of Electrical and Electronics Engineering. Since data is routed between devices in small chunk of data known as bits. This was then a standard measurement at the Internet inception as most of data files were significantly smaller.


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Each lesson in handwriting should start on a fresh new page, so the little one becomes enough room to practice. Every handwriting lesson should begin with the alphabets. Handwriting learning is just one of the most important learning needs of a kid. Learning how to read isn't just challenging, but fun too.
The use of grids The use of grids is vital in earning your child learn to Improve handwriting. Also, bear in mind that maybe your very first try at brainstorming may not bring anything relevant, but don't stop trying. Once you are able to work, you might be surprised how much you get done. Take into consideration how you feel about yourself. Getting able to modify the tracking helps fit more letters in a little space or spread out letters if they're too tight. Perhaps you must enlist the aid of another man to encourage or help you keep focused.
January Kindergarten Math Worksheets. Try to remember, you always have to care for your child with amazing care, compassion and affection to be able to help him learn. You may also ask your kid's teacher for extra worksheets. Your son or daughter is not going to just learn a different sort of font but in addition learn how to write elegantly because cursive writing is quite beautiful to check out. As a result, if a kid is already suffering from ADHD his handwriting will definitely be affected. Accordingly, to be able to accomplish this, if children are taught to form different shapes in a suitable fashion, it is going to enable them to compose the letters in a really smooth and easy method. Although it can be cute every time a youngster says he runned on the playground, students want to understand how to use past tense so as to speak and write correctly. Let say, you would like to boost your son's or daughter's handwriting, it is but obvious that you want to give your son or daughter plenty of practice, as they say, practice makes perfect.
Without phonics skills, it's almost impossible, especially for kids, to learn how to read new words. Techniques to Handle Attention Issues It is extremely essential that should you discover your kid is inattentive to his learning especially when it has to do with reading and writing issues you must begin working on various ways and to improve it. Use a student's name in every sentence so there's a single sentence for each kid. Because he or she learns at his own rate, there is some variability in the age when a child is ready to learn to read. Teaching your kid to form the alphabets is quite a complicated practice.


|FIBONACCI AND THE GOLDEN SECTION
This paragraph's links will take you to Dr Ron Knott's excellent University of Surrey website about Golden Section and the associated Fibonacci and Lucas number sequences, with their manyfold links to Nature and the Arts. The links below are to the informative biographical glosses on the University of St Andrews website.
In brief, Golden Section is the division of any length so that the shorter portion to the longer portion forms the same ratio as the longer portion does to the whole length. A classic golden section formation is the regular pentagram (5-pointed star), whose lines all intersect at their two points of golden section.
Fibonacci was Leonardo of Pisa (1175–1250), the mathematician who introduced Arabic numbers to Europe. His famous "Rabbit problem" involved the summative properties of the number series 1, 1, 2, 3, 5, 8, 13, 21 etc., which was named the "Fibonacci series" only much later by the 19th-century French mathematician Edouard Lucas. Lucas' name lives on in the associated "Lucas" summation series 1, 3, 4, 7, 11, 18, 29 etc. In both these series, as they progress, the ratio of successive terms comes ever nearer the exact value of golden section (0.61803398... or its inverse 1.61803398...).
Leonardo da Pisa himself didn't link Fibonacci numbers to golden section. One of the first people to do this in print was the Scots mathematician Robert Simson (in 1753, exactly between Bach's death and Mozart's birth). Simson hailed from the same Scottish village as Roy Howat (West Kilbride in Ayrshire). Simson's researches were based mostly on Euclid, whose Elements deal with golden section ("Extreme and Mean Ratio").
Edouard Lucas died in Paris in 1891, just a few years after Fibonacci numbers start to appear in Debussy's musical structures. One of Lucas's colleagues, Charles Henry, was the main æsthetic mentor to the Post-impressionist movement (notably to Seurat); during the 1880s and 1890s Henry wrote in arts and literary journals about the importance and function of ratios such as golden section.
In the 20th century golden section formed the basis of the architectural theories and practice of Le Corbusier (Charles-Edouard Jeanneret), and of influential æsthetic treatises by Matila Ghyka and Jay Hambidge. Ghyka's two-volume treatise Le nombre d'or (Paris, 1931) has a preface by Debussy's old friend Paul Valéry.
The photograph shown above of the memorial to Robert Simson, in West Kilbride cemetary, was taken by James Howat (Roy's late father, now buried in the same cemetary). The inscription on the plaque reads:
To Dr Robert Simson of the University of Glasgow, the Restorer of Grecian geometry and by his works the great promoter of its study in the schools. A native of this parish born 14 October O.S. 1687, died at Glasgow 1 October 1768 where rest his remains.
And buried learning rose
Redeemed to a new morn.
University of Surrey Golden Section / Fibonacci website


How do you subtract area in AutoCAD?
Select the objects that you want to keep, press Enter, then select the objects that you want to subtract. Objects in the second selection set are subtracted from objects in the first selection set. A single new region is created. You can only subtract regions from other regions that are on the same plane.
How do you add area in CAD?
For either command, when you see the text cursor, type Area: and a space. Right-click in the text area and choose Insert Field. In the Field dialog box, choose Objects from the Field Category drop-down list. This makes the field you want easier to find.
How do you use intersection in AutoCAD?
intersection command in AutoCAD
- Type INTERSECT and press ENTER.
- Select objects and press ENTER.
What is the unit of area in AutoCAD?
For example, if you select Inches, each drawing unit equals one inch. To scale objects that you insert into the current drawing from drawings with different drawing units, select Scale Objects Inserted from Other Drawings.
How do you add an area?
To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.
How do measure area?
For a square or rectangular room, you will first need to measure the length and then the width of the room. Then multiply the length and width. Length x Width = Area. So, if your room measures 11 feet wide x 15 feet long, your total area will be 165 square feet.
Does area add or subtract?
Adding and subtracting areas works just like adding and subtracting normal numbers. Make sure your units are the same first, though! To find the area of complex shapes, break them down into simpler shapes and add or subtract the areas.
How do you find the area of two triangles together?
To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram.
How do you solve for a shaded region?
The area of a rectangle is determined by multiplying its length times its width. The area of a circle is Pi (i.e., 3.14) times the square of the radius. Find the area of the shaded region by subtracting the area of the small shape from the area of the larger shape.


LeapFrog LeapStart Preschool Math Activity Book. Count on Scout and his pals to show you the fundamentals of beginning math with this fun-filled, interactive activity book for LeapStart™ the interactive learning system designed to get your child ready for school and life. LeapFrog® LeapStart™ Scout and Friends Math with Problem Solving Activity Book is jam-packed with 40+ replayable activities that engage kids ages 2-4 at the preschool level to keep them playing and learning for hours. With the LeapStart system, every page talks, sings and jokes with exciting audio interactions that bring learning to life. Join puppy pal Scout and his favorite friends as they play and explore counting, number recognition and problem solving. Count all the butterflies you can find, and then sing along to a cheerful ditty about butterflies. Trace numbers to make sure you have the right ingredients for your recipe, and then "bake" a cake. End the day with a dance party where you can learn numbered dance moves to boogie down. The LeapFrog LeapStart Preschool Math Activity Book Features: Join puppy pal Scout for a math adventure and learn about numbers and problem solving, while exploring a world full of friendly characters Teaches 12 preschool math and problem solving skills: matching quantities to numbers, counting to 10, comparing sets of objects and more Includes 40+ replayable activities and 25+ reward stickers Level 1: Preschool Perfect for ages 2-4 Works with all LeapStart systems. (Sold separately) LeapFrog designs and develops innovative, technology-based educational products and related proprietary content and learning toys and learning games. Toys > Category > Arts & Crafts, Educational Toys, Books > Learning & Educational Toys > Math, Counting & Time. Software > Video Game Software > LeapFrog Games.
* This offer may contain time-sensitive information and offers. Please check with Toys"R"Us to confirm actual price & availability.


Ph.D. candidate in math & applied math @ UoC
Hi there! This is my website. Here you’ll find some info about me and my work.
A few words about me…
I am a Ph.D. candidate in the Department of Mathematics and Applied Mathematics at the university of Crete in Heraklion under the supervision of Prof. Spyridon Kamvissis.
My research interests lie in the field of mathematical physics; the interactions between physics and mathematics.
In my spare time, I like listening to music, playing the saxophone, watching movies or theatrical plays, reading and trekking.
Here on the left, you see me in “Skepasmeno falls”; a breathtaking place hidden in a small gorge located close to my hometown of Velventos in the northern part of Greece.
A short CV
Here, is my CV.
As I mentioned before, I am a huge fan of the scientific area lying in the midst of mathematics and physics. The fact that fascinates me the most is trying to get a grasp on problems arising in areas like QM, GR, wave propagation, etc. using mathematical tools like ODE & PDE theories, functional, real and complex analysis, differential geometry, topology and even algebra.
Currently working on…
⦁ Project 1: Soliton Resolution Conjecture
⦁ Project 2: A WKB problem for the Zakharov-Shabat system with analytic potential and fast phase.
⦁ Project 3: Asymptotic analysis of a Dirac operator having a real potential with multiple wells and barriers.
⦁ Asymptotic analysis of Schrödinger & Dirac (or Zakharov-Shabat) operators; their semi-classical (WKB or LG) limits of bound states and eigenvalues (with Spyridon Kamvissis) (arXiv).
Il libro della natura é scritto in lingua matematica.Galileo Galilei


As a student, struggling with math can be incredibly frustrating. However, by implementing effective strategies and adopting a positive mindset, you can enhance your math skills and achieve better grades. In this article, we will explore 7 practical tips that can help boost your math grades. So, let’s dive in!
1. Pay Attention in Class:
Attentiveness is key when it comes to learning math. Concentrate on your teacher or professor during lectures, ensuring that you grasp the concepts being taught. Take comprehensive notes, ask questions, and actively participate in class discussions. Being engaged will provide a solid foundation for understanding complex topics.
2. Practice Regularly:
Mathematics is a subject that requires consistent practice to improve. Set aside dedicated time each day to work on math problems and exercises. Revisit and revise concepts regularly, even when you feel confident in your knowledge. By practicing consistently, you will reinforce your understanding and identify areas that may require further attention.
3. Seek Help When Needed:
It is essential to recognize when you need additional support. Don’t hesitate to approach your teacher or classmates for help with math problems or concepts you find challenging. Additionally, consider forming study groups where you can work with peers, discuss problems, and share insights. For more complex topics, you can even pay for math homework assistance from online tutors or homework services, ensuring that you receive personalized guidance.
4. Utilize Online Resources:
In today’s digital age, access to online resources is virtually endless. Numerous websites and online platforms offer free math tutorials, practice problems, and interactive exercises. Take advantage of these resources to supplement your learning. Explore websites that offer step-by-step solutions to common math problems, engage in virtual math games, or download math-related apps on your smartphone to make learning more accessible and enjoyable.
5. Practice Visualization:
Mathematics often involves conceptualizing abstract ideas. Develop your visualization skills by creating mental imagery to better understand complex problems. Visualize geometric shapes, graphs, and equations to gain deeper insights into their properties and relationships. Visualization can be especially helpful in geometry, algebra, and calculus, enabling you to approach problems from multiple perspectives.
6. Find Real-Life Applications:
Mathematics has many real-life applications, even outside the classroom. Look for opportunities to apply mathematical concepts in everyday situations. For instance, when shopping, calculate discounts, analyze prices, or estimate costs. Engaging with math in practical contexts will reinforce your understanding and make it more relatable and interesting.
7. Maintain a Positive Mindset:
Believe in your abilities and maintain a positive attitude towards math. Avoid telling yourself that you are “not good” at math, as this negative self-talk can hinder your progress. Embrace challenges as valuable opportunities to learn and grow. Celebrate small victories and stay motivated throughout your math journey.
Improving your math grades requires commitment, regular practice, and a positive mindset. By following the strategies outlined above, such as paying attention in class, practicing regularly, seeking help when needed, and utilizing online resources, you can bolster your math skills and achieve better grades. Remember, persistence and determination are key to conquering any math-related challenges you may face. So, embrace the journey and enjoy the process of mastering mathematics!


I love symmetry. It’s fun to arrange a room in a way that it is the same color or shape. It’s the same shape as the furniture. It’s the same shape as the floor plan. It’s the same shape as a wall. It’s the same shape as a window.
All of this is a lot of fun to me. I’m not sure how to describe it, but it is. I just think it’s interesting. It is the idea of a puzzle, the idea of a puzzle, and the idea of a puzzle together—all of these things make up a puzzle. The puzzle is not about solving a puzzle, but about solving it. It’s the idea of a puzzle, not a puzzle.
The idea of a puzzle is to understand just how much you’re meant to be, which is really the key to how to be a good cop. If you’re trying to figure out what’s really a puzzle, you’re trying to figure out how to think about it.
It’s also the idea of a puzzle that we have to think to be a good cop.
A good puzzle is one that keeps you on your toes, and to keep you on your toes it can be about trying to work out the solution. In the case of a puzzle, the idea is that you do your best to understand the rules and see how your best ideas fit in. If youre trying to find the answer to a puzzle, you are doing this in order to figure out how well your ideas fit together.
One of the most important concepts to learn about is the concept of symmetry.Symmetry is a very important concept to learn because you can use it to figure out things that are otherwise very confusing. For example, you can start with a picture of your desk and see how it looks from any angle. If you take the desk straight up, you can see that the desks are all the same shape, but if you take the desk straight down, you can figure out that they aren’t.
In order to take out the desk, you have to figure out the shape of the desk and look for the desk that looks like a pair of scissors with the letters c,d and e. Then you need to figure out the shape of the person you are trying to kill. Obviously, you can get around this problem by using the trick of following the easy-to-follow directions for finding the desk you want to kill.
I think a lot of people are wondering how this is connected to the game’s theme. Well, it turns out that the desks in symmetrical patterns are actually the actual patterns used in the game’s game. But the real point is that the desks have the same shape, but they are not the same things. The desks are the building blocks of the game, and the patterns are the various rooms that you can use to kill the Visionaries.
That’s right, it really just depends on when and where you go. If you’re on the island, you can have the desk, and that desk is actually the first room on the island you open. The second room you open up is the room where you have to kill the Visionaries, and it is the only way to kill them because they use different patterns to kill your enemies.
It’s actually kinda funny how symmetrical and random the patterns are. You could go from a pattern that looks like a clock to the other. You could go from a pattern that looks like a clock to a pattern that looks like a broken clock. The pattern that looks like a clock is actually a random pattern, and the pattern that looks like a broken clock is actually a clock.


Parents' Guide to Student Success
A link to Common Core Standards for elementary students is provided by the National PTA via
The guide provides parents with an overview of the Mathematics and English/Language Arts/Literacy Common Core Standards for grades K-6. Parents will be able to learn the key skills children will learn in these subjects in each grade. The guide is based on the new Common Core Standards recently adopted by over 40 states, including Kansas. During the 2011-2012 school year, Central Schools is beginning the transition to these standards while still focusing on the standards tested on the yearly state assessments. If you have questions, please call the school office.


Review: Hammer & Premium auction premium calculator app
If you have problems calculating what you are paying for – or taking total prices up to hammer price – the Hammer & Premium App is for you.
Hammer & Premium describe the app as the: “art auction adding machine for the modern magpie.”
The app has a very clean look and is simple to use. Once installed you can load the app quickly then select the function before entering the required data for the app to calculate the relevant numbers – either the premium price or the hammer price.
The interface for both functions is very similar. The app offers a long drop down list of auction houses to select from, the user then enters either the hammer price or the premium price and set the vendor’s commission rate, the App will then calculate the hammer price, net to seller, buyer’s premium and vendor’s commission.
The app was first released in December 2014 and has since had several updates which have added more functionality to the app, including adding further auction houses. There is also an online version of the app offering the same functions but which can be viewed in a browser.
Currently Hammer & Premium is only available in on Ipad or Iphone in English and German, and can be downloaded for free from the App store.


Standard Deviations in Blackjack and Roulette
A casino game is a game of chance when a player bets on the outcome of a random event. For example, the player may bet his money on a machine that offers a jackpot of one thousand dollars. If he wins that amount, then he gets the jackpot. A similar thing is true for other casino game outcomes, where a person wins money by playing his favorite game. Of course, there are many other styles of casino games too.
You can find basically three 맥스 카지노 types of casino games: table games, gaming machines, and random number generators. In table games, it is possible to play with a couple of cards comprising from four to nine numbers, where each card represents among the numbers that are displayed on the wheel. Thus, a player is able to manipulate the odds that include these cards. In gambling, the odds refer to the chance of a win; thus, one can say that gambling is really a form of gambling, since there is always the possibility of an absolute ticket. Gaming machines may also be considered gambling, as they involve using machines that spin and present the outcome as the player bids and pulls the lever. Lastly, random number generators are accustomed to generate numbers that are random and appear in sequence, either randomly generated.
The most popular baccarat game is undoubtedly video poker. As video poker became popular among casino game players, there have been also a lot of people who wanted to learn to play it. Learning how exactly to play video poker might take some time, but it is a fun casino game to play, as it allows the players to mix luck with strategy.
There are plenty of other types of casino games on the market. One of these is craps, that is considered the casino game for gamblers who would rather play without any risk. Craps is a type of betting where one pays money hoping that they will get a specific card. You can find slot machines as well as baccarat and roulette available, and them all offer a chance to earn money by betting on the possibility of getting specific cards. Roulette is available on many machines as well, though not all slots accept this game.
Another popular casino game which might be played at land-based casinos or online is poker. Poker is a card game in which a player enters an area, bets some money and then tries to obtain all their cards (all of the cards in the deck) into the pot prior to the other players do. This is usually a simple game that could be easily explained to children, since it is actually an easy task to grasp. This is a favorite among casino avid gamers, and a lot of websites have game sections that enable you to play for free. You can find other types of cards available aswell, including keno and blackjack.
A straightforward game like roulette will not be something that beginners should start learning, nonetheless it is actually a good notion to get experience in this subject. Most casinos could have a particular table for roulette gambling, since this game involves so many possible outcomes. A new player can find out about standard deviation and try to make a profit from them by playing a few hands here and there.
Video poker has become extremely popular in recent years because it offers the possibility to play casino games online in a fast, convenient way. The Internet has made it easier than ever before for players to reach a high number of dealers with just a couple clicks of the mouse. Which means that video poker is one of the fastest-growing casino games, allowing players to put bets without having to wait very long. Blackjack and roulette may also be excellent options in order to find out more on blackjack strategies, although latter game involves a lot of luck, which may make it too complex for a novice’s tastes.
The basic idea behind the typical deviation and the binomial distribution is by using probability theory to estimate how much cash you will probably win or lose on a regular basis. This allows one to calculate the expected outcomes of any given casino game based on the standard deviation of results. For example, if you want to know how much money you will probably win at blackjack, standard deviation tells you how often you can expect to lose the same amount, or to come out on top. It’s a fantastic tool for a casino game enthusiast, even those people who are just studying it.


So I have been struggling with being boring. I decided to homeschool so that my kids would not be put through a school mill and just do busy work. I really wanted my kids to have a passion for learning and as I have homeschooled through the years I have only been able to accomplish the bare minimum. The kids have enjoyed it though. So we are homeschooling with another family this year as I have mentioned before and I found myself just being sort of boring. It has taken me till the middle of October to figure out that I just don't care how fast they get through math, or science, or whatever it is if they do not have a passion for doing what they are doing. Why plug and chug through math just to get to the next lesson? Is that so they can say they are on lesson 44? What if they don't own that information? And.......being the random person that I am, I want to do some things (finally) with math that are FUN! That challenge their brain cells to figure faster and logically. So....we are playing math games and doing math in sort of "don't move on unless I know you understand your mistake" sort of way. I still get blank looks but at least I have noticed recognition and enthusiasm on their faces more than before.
I am still processing Science and History strategies to make things more interesting. Some lessons are very interesting and some are so far removed from their life knowledge, especially in history, that they just nod their heads at me without realizing how these events effected the world at large. Hmmmm........stay tuned. I will process this someday and perhaps blog on how to make these more interesting.


About Zapata Computing:
Zapata Computing, Inc. is a quantum software, services, and applications company with a mission to accelerate the quantum revolution. We are developing a quantum workflow platform to solve critical problems across a wide range of industries. Zapata’s quantum platform Orquestra® combines a powerful software platform and quantum algorithm libraries to deliver real-world solutions across a full range of classical and quantum technologies.
About the Job:
Zapata Professional Services works with customers of all shapes and sizes in all verticals, on a variety of interesting use cases. Zapata Professional Services exists to support the development of our customers’ vision, accelerate customers’ time to value and drive a multitude of customer adoption scenarios. As an application scientist in the team, you will interact with our clients to understand their use cases and work along with other scientists and engineers at Zapata to develop and apply optimization algorithms to tackle customer’s computational challenges.
- Communicating closely with industry clients to understand their optimization needs
- Implementing, testing, and deploying optimization algorithms for solving large-scale problems of industrial interest.
- Conducting numerical simulations to benchmark algorithm performance.
- Analyze output data and present analysis to team members and clients.
- Participate in fast-paced research in machine learning and quantum computing applications, with emphasis in quantum, quantum-inspired and classical algorithms for improving upon state-of-the-art optimization techniques.
- Familiarity with algorithms for solving combinatorial optimization problems, including quantum and quantum-inspired techniques.
- Proficiency with state-of-the-art optimization software and techniques.
- Experience programming with scientific software such as Python, C/C++, or Julia.
- Experience applying optimization techniques to industry problems.
- Ph.D. in in Physics, Computer Science, Mathematics, Electrical Engineering or a related discipline
- Programming experience with quantum software such as PyQuil, Cirq, Qiskit, Q#, etc.
- Experience in Machine learning techniques applied to industry problems.
- Global remote
To apply for this job email your details to email@example.com


We see Year 7 as an introductory year, laying the foundation for secondary school. Subjects offered at this level include English, Maths, Art, Science, Humanities, French, Dance, Music and Philosophy. Students have several free periods a week, to enable them to explore their own interests.
In Years 8, 9 and 10, the only mandatory subjects are English, Maths, and Music. All others are electives, involving choices from VCE and other subjects which include Beginners French, Intermediate French, Advanced French, Art, Drama, Music, PE, Chemistry, Biology, Physics, Forensic Science, Outdoor Education, Dance, “Nerd Club” (ICT), Chinese, Philosophy and Anthropology, Motion Media, Guitar Club, and History. Classes in Years 8, 9 and 10 are frequently grouped according to subject choice, allowing for greater diversity of interaction, and a greater range of electives.
We encourage keen and able students in Years 9 and 10 to tackle at least one VCE subject during this time. In exceptional circumstances, Year 8 students may also take on a VCE subject.
During free time, many optional activities are offered, including sport, martial arts, chess and writing workshops.


This is a bit a random question, but the answer has been bugging me for a long time, ok so….
On a microwave, if you push 60, then it will cook for 60 seconds or one minute. And if you also press 1:00 it will cook for one minute, or 60 seconds, right ?
Ok, well, this is my question is…
If you add 1:00 + 1:00 = 2:00 right ? So your food will cook for a total of two minutes. But if you add 60 seconds + 60 seconds it will only cook for one minute and twenty seconds. Eventhough 60 seconds is one minute ? I know, this is confusing question.
I guess to put into simplest term, how come 1 minute + 1 minute = 2 minutes but 60 seconds + 60 seconds is only one minute and twenty seconds ?


Few days back we were working on using direction cosine matrix #DCM for calculating the orientation of a #UAV given the angular velocity vector. We decided to publish it hopefully it will be usefull to the students of learning integrated navigation.
So forexample we are given an angular veolcity vector:
|−0.10 · cos (Ω1t)|
where Ω1 = −4 rad/s and Ω2 = 1 rad/s.
We would like to find the spacecraft’s orientation (relative to it’s initial state) at t = 1000 s.
Here is the solution in Matlab:Avionics-UAV-Orientation


Nicholas Bennett received his BA in Mathematics from the University of the South (1991), and his PhD, also in Mathematics, from Yale (1997). His interests have always involved applied math in one form or another. Beyond the training he received at Sewanee and at Yale, Professor Bennett feels the most important formative influences on his career were a semester study abroad experience at Budapest Semesters in Mathematics, summer Research Experience for Undergraduates (REU) at the University of Tennessee, two summer internships in the Director’s Summer Program at the National Security Agency, and the two summer internships at Schlumberger. The latter paved the way for his current employment as Research Scientist for Schlumberger.
Prof. Bennett’s work is quite interdisciplinary (math, acoustics, electromagnetics, geology, computer science) and so requires considerable technical collaborations. An important skill he has developed over the years, and recommends to others, is to learn how to present very technical work to a general audience. He is happy to discuss his public speaking techniques.


Designing a ring that looks like a closet has never been so easy!
We’ve all been tempted to design something like this, only to realise that it’s not actually that easy.
Here’s the simple step-by-step guide to designing a ring with Clothes.
Create a sketch of the ring design.
Create an outline of the design, and then draw a line to mark the point where the design starts.
Find the ring dimensions.
Find where you want the top of the circle to go and cut the ring into a 3/4-inch thick circle.
Mark the location of the pocket.
Make sure it’s in the middle of the circumference.
Measure the distance between the pocket and the top.
Find this number and draw a circle in the centre.
Add the ring shape.
Use your calculator to find out how many inches you need to add between the top and the pocket, and how much space is left over.
Create the pocket with your ring design: draw two lines across the top, one on each side.
Fold the pocket in half.
Create three holes.
Fill in the gaps with buttons, and fold the pocket back into the top half.


Math In Balance is an educational app created to help anyone who struggles solving single variable equations. Users can select from one of three characters to follow a unique path to solving equations. This app is formatted so the user is presented with a linear equation and asked to solve for x. Using the interactive scale, users balance the equation as a visual reminder that what is done to one side must also be done to the other. Once the problem is solved correctly, the user gets a stamp and can move onto the next equation. Each path has 10 equations and can be completed multiple times with different problems appearing each time.


In today’s digital world, information technology has become an integral part of every industry, from healthcare to finance to education. However, many people are still under the misconception that information technology requires a strong foundation in mathematics. This article will explore the question; does information technology require math?
Mathematics and Information Technology:
There is no denying that mathematics plays a crucial role in information technology. In fact, it is the foundation on which many of the technological advancements we enjoy today have been built. From algorithms to cryptography to compression techniques, all these advancements require a deep understanding of mathematical concepts and principles.
While many people assume that coding and programming are synonymous with mathematics, the truth is that coding actually involves more logical reasoning and problem-solving skills than math. While it is true that programmers must use basic arithmetic, the majority of their work centers around organizing code in a logical and precise way.
Database management is another area where mathematical skills are required, but not to an extent that would exclude someone who is not mathematically inclined. The role of a database manager largely revolves around organizing data in a way that is easy to retrieve and analyze, and understanding basic concepts such as data mining and data warehousing.
Networking is another area where mathematical concepts are applied but not to an extent that would turn away individuals without a strong mathematical background. Network engineers primarily work with switches, routers and various networking protocols. While some basic math is required to configure IP addresses and subnet masks, most of their work is focused on understanding network topologies and performance metrics.
Machine Learning and Artificial Intelligence:
In recent years, machine learning and artificial intelligence have become hot topics in the field of information technology. Both of these fields require a strong understanding of statistics, linear algebra, and calculus. However, the reality is that these concepts can be learned alongside machine learning and artificial intelligence to allow anyone to become proficient.
In conclusion, while information technology may require some level of mathematical skills, it does not require an extensive or advanced knowledge of mathematics. There are various areas of information technology, such as coding, database management, and networking, where mathematical concepts are applied but not to an extent that would exclude someone who is not mathematically inclined from entering the field. It is important to acknowledge that having basic mathematical skills can indeed provide an advantage in certain areas of information technology, but it is not a requirement to enter the field or be successful in it.


Differential Equations Tutors in Simi Valley, CA
Find Private & Affordable Differential Equations Tutoring in the Simi Valley Area!
University of Hawaii at Manoa - BS, Meteorology , Missouri State University - Master of Science, Geoscience
UCLA - BS, Mathematics
Cal State Northridge - BS, Mechanical Engineering
University of California, Berkeley - BA, Applied Mathematics and Geophysics
University of California, Santa Barbara - BS, Physics
University of California Los Angeles - BS, Astrophysics
University of California Santa Barbara - BS, Computer Science
California State University-Northridge - BS, Physics , San Diego State University - MS, Physics
Cornell University - BA , Near Eastern Studies , Pardee RAND Graduate School - PhD, Policy Analysis
University of California-Los Angeles - BS, Applied Mathematics and Business Economics
UCLA - BS, Psychobiology
University of Virginia-Main Campus - BA, Astrophysics
Ken G., Tutor in Math, Physics and Chemistry • Education and Work Experience Ken has a BS in Statistics and Physics from Stanford...
MS, Chemical Engineering, USC; GPA = 3.4 MBA, UCLA - Anderson; GPA = 3.7


We saw last week that 300 is an “abundant” number, and that, from the list of abundant numbers in the top 100, it would seem that they are all even; but it is not like that: there are infinite odd abundant numbers, although if we look for them by going through the list of natural ones one by one it will take a long time to find the first and smallest of them, which is 945. To check the infinity of the abundant numbers, both Even and odd, it is enough to see that all multiples of an abundant number are, in turn, abundant (why?).
In addition to abundant, the number 300 is the sum of ten consecutive primes:
300 = 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47
It is also a polygonal number: specifically, 300 is the 24th triangular number.
We talked last week about regular and semi-regular tessellations, and since in the second case we can combine all the regular polygons we want, of any size and in any proportion, it would seem that the possibilities are many, if not unlimited; but this is not the case if the pattern is regular, that is, the same in each vertex of the configuration. In fact, there are only 8 semi-regular tessellations, which are identified with this notation:
184.108.40.206.6, 220.127.116.11.4, 18.104.22.168.4, 22.214.171.124, 126.96.36.199, 3.12.12, 4.6.12, 4.8.8
What do these numbers mean?
But the many geometric mosaics that we find in all ages and in all cultures do not adhere to regular polygons. Let’s see some of those formed by a single type of tiles, all the same.
The most abundant tiles, along with the square ones, are the rectangular ones, which we see in all kinds of tiles and brick constructions. And it is evident that any parallelogram can also tessellate the plane, since we only have to extend the sides of a seminal parallelogram and draw the appropriate ones parallel to them, equidistant from each other, to form a homogeneous mesh.
And since with every triangle a parallelogram can be formed by attaching another equal triangle to it, any triangle can tessellate the plane.
Less obvious is that with any quadrilateral, convex or concave, the plane can also be tessellated. How is it demonstrated?
With some irregular hexagons the plane can be tessellated, but not with all. With which ones is it possible?
The Islamic prohibition to reproduce human figures or other animals favored the development of a wide iconography based on geometric figures and repetitive patterns, as can be seen in great historical monuments such as the Alhambra (whose mosaics and ornamental motifs were studied in depth by the Dutch engraver MC Escher). In Arab mosaics we find common figures in other cultures, such as stars (5, 8 or 12 points, among others) or rhombuses, and other very characteristic ones, such as a peculiar pentagon with five equal sides, with two right angles, two of 108º and one of 144º, which gives rise to the so-called Cairo mosaic, as it is frequently seen on the streets of the Egyptian capital. It is usually rounded, and I have done so, the value of the angles of 108º and 144º, can you find their exact value?
The one with the Cairo mosaic is one of the 15 irregular pentagons with which the plane can be tessellated. It has not been shown (that I know of) that there are none more, so I invite my astute readers to find a 16th type of tessellation pentagon, or to prove that it does not exist.
As for the title of this installment, can we take it literally? Is the number of possible mosaics really infinite?
Carlo Frabetti is a writer and mathematician, member of the New York Academy of Sciences. He has published more than 50 popular science works for adults, children and young people, including ‘Damn physics’, ‘Damn maths’ or ‘The great game’. He was a screenwriter for ‘La bola de cristal’.


Title：Quantum Chaos in Topologically Massive Gravity
Online report（ZOOM ID：815 1227 7968）
Abstract：Chaos is ubiquitous to a wide range of physical systems with large number of degree of freedom and is crucial to thermalization and relaxation of the system. The exponential growth of out-of-time-order correlators and pole-skipping in the retarded two-point correlation functions of energy density are two different signatures for quantum chaos. We study quantum chaos of rotating BTZ black holes in topologically massive gravity. We discuss the relationship between chaos parameters including Lyapunov exponents and butterfly velocities from OTOC and from pole-skipping analysis. We find a partial match between pole-skipping and the OTOC results in the high temperature regime. We also find that the velocity bound puts a chaos constraint on the gravitational Chern-Simons coupling.


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The information in this article is general only, past investment performance does not guarantee future investment performance, before you make any financial decision you should seek the advice of a qualified professional
Today I’m going to talk about a concept that not many people know about
This thing I’m about to talk about will explain to you that when you invest your money over time you actually end up with more than you thought you would!
How is that possible? You ask.
I will explain now, I call this the velocity of money.
Ok, so when people do a calculation on what their investments could turn into over time when they use compound interest calculators what they don’t realise is that your income at your job or business goes up over time.
YOUR INCOME GOES UP OVER TIME which is inflation really..
So let’s say your income goes up over time at an average rate of inflation of say 3% a year.
Well then the amount you invest goes up each year with inflation!
You might of calculated that your investment of say $100 a month would turn into x amount over 10, 20 years but with your income going up you would have invested a lot more and ended up with a lot more!
I will provide an example now how simply getting pay increases over time with inflation causes you to END UP WITH AN EXTRA 10% at the end of the 10 year investment term.
Ok, so in this example I will explain how investing $100 a month for 10 years at 8% (3% inflation + 5% dividends reinvested which is basically what the stock market returns) in two different situations
The first situation is how people normally calculate it, with no increase to deposit amount and the second situation is with the increases in pay and therefore deposit amount.
Ok, here’s how the first situation would look.
Investing $100 a month for 10 years at 8%
After 10 years you end up with $17,383 or $12,935 if adjusted for inflation (3% a year)
Now the second example, the deposit amount each year increases with pay rises from inflation
Year 1. $100 per month = $1,200
Year 2. $103 per month = $2,532
Year 3. $106 per month = $4,006
Year 4. $109 per month = $5,634
Year 5. $112 per month = $7,428
Year 6. $115 per month = $9,402
Year 7. $118 per month = $11,570
Year 8. $121 per month = $13,947
Year 9. $124 per month = $16,550
Year 10. $127 per month = $19,398
SEE THE DIFFERENCE! $19,398 versus $17,383!
That’s a difference of $2,015 which is a 10.39% increase!
See how the velocity of money works?
Imagine if you took pay rises into your own hands and seeked a higher paying job or did well in your own business, you could turn that 10% into 30%, 50%, 100% or more!
See how it works guys? Keep it in mind next time you calculate your investment goals.


…..Until my next math book comes.
Today, on November 24th 2009, I Cassia, finished my math book!
My certificate. 😀
In the math program were using right now, there is a certificate at the end of each math book .
My finished math book! Yes, that is a calculator in the upper right corner, but don’t worry, I wasn’t cheating with it. 😀
I am very glad to be out of this math book, I’ve been in it since March of 2008! But, I am looking forward to my next math book (at least for now :D) because it will be new I guess.
Ta Ta For Now!
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(An excerpt from a family conversation over email discussing this article: http://www.slate.com/articles/life/education/2016/03/algebra_ii_has_to_go.html. In it the author argues that Algebra II doesn’t belong in the standard high school curriculum anymore. She says that there are other more useful courses that could be substituted (statistics for example), and that it is a crippling requirement for high school graduation. Many high school students fail to graduate solely because of the Algebra II requirement.)
“I personally was never bad at math, but during high school I hated taking the liberal arts classes. English in particular I despised - perhaps partly because of my consistent score of 88% on every essay I wrote ever. However some of the arguments made could be swapped around to attack other subjects - why do we take English and read old books if it doesn’t affect our careers?
During my high school career this is probably what I would have felt, but after taking a couple of ‘gen ed’ courses in college I think I see things differently. A lot of my classmates try and do anything to not take the gen eds - APs, summer classes, online courses, go looking online to see which professors give out the most A’s. I think this is such a waste. My gen ed courses have been some of my favorite and most interesting courses I’ve taken - whether it be the history of masculinity and femininity in the US, American literature, Texas history, or creative problem solving. Once upon a time college was about learning to think and learning to learn (a liberal arts education), and I still believe in that dream.
College has moved pretty far in the direction of vocational schools now. Parents encourage kids to think of them like that, kids encourage their peers to think like that. Like I said earlier most of my classmates disdain their gen eds.
I would argue that Algebra II could be considered as one such ‘mind expanding’, ‘liberal arts’ gen ed. As her husband argues, well taught math encourages people to think differently. However the caveat here is that the math has to be well taught. I think math is a very easily mistaught. Math can be very insightful as a subject, but most people don’t know how to teach it correctly. I firmly believe that anyone can learn math, but most people ‘are not math people’ because their teachers were poor.
Does it make sense to teach algebra II to a student who doesn’t have the background skills to be able to learn it? No. But I would argue algebra II is not the problem - the system of math education is. Unfortunately that’s probably not going to be solved anytime soon.”


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In The Theory of Blackjack by Peter Griffin, an excellent book for potential card counters, he has a small section about counting baccarat. In an eight hour day you might make three bets. Dream Job or Nightmare? Notify me of new posts by email. If you want to practice card counting Baccarat, then you can do so sitting somewhere with a single deck of cards.


Principles of Aerostatics
Principles of Aerostatics presents the complete theory of static lift for airships, aerostats and balloons. Concepts are laid out, and building on the derivation of temperature, pressure, density and humidity in the atmosphere and the gas laws, formulas for static lift are derived. The variation of lift with atmospheric and airship parameters, climb and descent, and flight above pressure height are then explored. Both SI and United States Customary Units are employed throughout, and worked examples and calculator programs are provided. The mathematical processes can followed by a reader with an understanding of high school algebra.
"This is an excellent and unique work bringing the strands of basic theory together and rendering them into a workable series of mathematical expressions which can be used by any individual with a hand held scientific calculator. It is a most significant contribution to the LTA industry."


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Posted by Deva Jasheway
I signed up for an online class that started at the beginning of the month. I watched the first three video lectures right away, but then I forgot about it for the rest of the week. Each time they post the next week’s lectures they send an email. I got that email as each Sunday passed, putting off watching the videos, and finally, yesterday, went and watched the rest of the first weeks’ videos. The first four weeks are posted now.
The first videos I watched were ok. I generally understood what they were talking about and I figured they’d elaborate more in later weeks. Then the fourth and fifth, or fifth and sixth–I’m not sure, counting is hard–videos came along with equations and stuff, and all of a sudden I’m like “Uh, what?”
I’m not good with math. I can wrap my head around equations but only if each part is explained to me in detail, usually, and did I mention I haven’t actually done any math since high school, where I haven’t been for almost nine years? I was pretty lost. I felt that anything that they lingered on was stuff that was ridiculously easy to understand, but they sped through the equations without actually explaining how to use them. I really wanted this class to be a success, but if I watch the second group of videos and can’t get it, I might have to unenroll. I’m sure this will be largely because I put off watching the videos and therefore didn’t give myself enough time to study the stuff. But I thought we were going to be talking about theoretical stuff, not making calculations, so…
I’m starting to think that online classes don’t work for me, particularly if it’s just a free class that I’m not taking for a grade. There’s just about no accountability and that, ODDLY ENOUGH, is the same reason I never get any writing done.
I don’t know. There’s a class on the music of The Beatles starting soon, so maybe I should just take that one.