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In Karl Rubin showed that for elliptic curves defined over an imaginary quadratic field with complex multiplication by , if the -series of the elliptic curve was not zero at , then the -part of the Tate-Shafarevich group had the order predicted by the Birch and Swinnerton-Dyer conjecture, for all primes. In Andrew Wiles, Christophe Breuil, Brian Conrad, Fred Diamond and Richard Taylor proved that all elliptic curves defined over the rational numbers are modular the Taniyama-Shimura theorem , which extends the previous two results to all elliptic curves over the rationals.
Nothing has been proved for curves with rank greater than 1, although there is extensive numerical evidence for the truth of the conjecture.
Papers, Preprints and Lecture Notes
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AoPS Wiki. Page Article Discussion View source History. Background In Louis Mordell proved Mordell's Theorem : the group of rational points on an elliptic curve is finitely generated. An L-function can be defined for an elliptic curve E by constructing an Euler product from the number of points on the curve modulo each prime. History In the early s Peter Swinnerton-Dyer used the EDSAC computer at the University of Cambridge Computer Laboratory to calculate the number of points modulo denoted by for a large number of primes on elliptic curves whose rank was known. From these numerical results Bryan Birch and Swinnerton-Dyer conjectured that for a curve with rank obeys an asymptotic law Initially this was on the basis of somewhat tenuous trends in graphical plots; which induced a measure of scepticism in J.
Literatura iz eliptičkih krivulja i njihove primjene u kriptografiji
Category : Number theory. Subscribe for news and updates. Login Cancel Stay logged in. Create a new account Lost your activation email? This is technically more sophisticated but I believe there are also implementations.
The best practical solution is to have someone else do the work. You can look up the curve in Cremona's tables , if it is not too large. It is misleading to say "algorithm", really. There are probabilistic algorithms, and then hard cases evidence of a point of infinite order that is hard to find.
I think of Andrew Bremner as one of the experts on the highly numerical side, and you should add his name to John Cremona's. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered.
- Call to Battle (Scrapyard Ship, Book 7);
- Additional Material for the Book.
- Elliptic curves — Sage Constructions v;
- Black Hills.
Algorithms for finding rational points on an elliptic curve? Ask Question.
Asked 8 years, 11 months ago. Active 6 years, 7 months ago. Viewed 7k times. Andrej Bauer Andrej Bauer Section 4. But if one is only interested in the practical matter of finding points, rather than the well-foundedness of the methods, then there are algorithms. More precisely, if you believe the Birch and Swinnerton-Dyer conjecture, then there are efficient algorithms that are guaranteed to terminate.
Oct 13 '10 at I was talking about modular symbols, which were used by Cremona to generate his database of elliptic curves, but this has nothing to do with the present question. Sorry about that, I should stop posting so late at night! Jamie Weigandt Jamie Weigandt 2, 1 1 gold badge 23 23 silver badges 35 35 bronze badges. See the note here: warwick.
This makes life simpler for me, which his a good thing at least for me. I still use mwrank stand-alone myself hardly surprising. Secondly, Jamie's remark about mwrank in Sage being more up to date is simply nonsensical. I'm sorry was confused about that. Sorry about that, I should stop posting so late at night!
Jamie Weigandt Jamie Weigandt 2, 1 1 gold badge 23 23 silver badges 35 35 bronze badges. See the note here: warwick.
[PDF] Rational Points on Modular Elliptic Curves - Semantic Scholar
This makes life simpler for me, which his a good thing at least for me. I still use mwrank stand-alone myself hardly surprising. Secondly, Jamie's remark about mwrank in Sage being more up to date is simply nonsensical. I'm sorry was confused about that. Robin Chapman Robin Chapman All the notation and equations in the presentation in Silverman-Tate really obscure what is going on, in my experience. Felipe Voloch Felipe Voloch The descents as in Robin's answer tell us that in order to find rational points on an elliptic curve, we better search on one of its torsors.
But in the end, we have to do some "brutal search" and that is where the crucial improvements in ratpoints are useful. But all of them only work when the analytic rank is 1. Most of this is implemented in magma and lots of it in sage. Inputing "import sage. Michael Stoll wrote a paper about this, but I can't find it online anymore it vanished from his website , so here is a temporary link: wstein.
If you type print EllipticCurve [a1,a2,a3,a4,a6]. For more about elliptic curves over the rationals in Sage, see this page: sagemath. Charles Matthews Charles Matthews They often rely on unproven conjectures, but they happen to work very well in practice. Also, probabilistic algorithms are referred to as "algorithms", just as deterministic ones, and I don't quite see what is misleading about this terminology.
Of course it is misleading here to mix up different kinds of algorithms. Brute force search will find a rational point on a curve if it is exists partial correctness. A correct algorithm is what people generally mean by something being "algorithmic". A good probabilistic algorithm is typically what is sought in computational number theory, and a good algorithm with correctness proof conditional on some known conjecture is of real interest.
What the heck are you talking about? Without making one of those assumptions, we still don't know.


000744 EGHWERIDO J T (Federal Univ of Petroleum Resources, Effurun, Nigeria) : The alpha power gompertz distribution: characterization, properties, and applications. Sankhya A 2021, 83-A(1), 449-75.
A new three-parameter model called the Alpha power Gompertz is derived, studied and proposed for modeling lifetime Poisson processes. The advantage of the new model is that, it has left skew, decreasing, unimodal density with a bathtub shaped hazard rate function. The statistical structural properties of the proposed model such as probability weighted moments, moments, order statistics, entropies, hazard rate, survival, quantile, odd, reversed hazard, moment generating and cumulative functions are investigated. The new proposed model is expressed as a linear mixture of Gompertz densities. The parameters of the proposed model were obtained using maximum likelihood method. The behaviour of the new density is examined through simulation. The proposed model was applied to two real-life data sets to demonstrate its flexibility. The new density proposes provides a better fit when compared with other existing models and can serve as an alternative model in the literature.
5 illus, 4 tables, 31 ref


The Registered Voter Economic Confidence Index (RVECI) is conducted monthly by Big Data Poll for the Public Polling Project. It includes interviews from at least 2,000 registered voters nationwide via online panel. The sampling error is ± 2.1% at a 95% confidence interval.
Registered Voter Economic Confidence Index Methodology
Voters are asked to assign either a “positive”, “neutral”, or “negative” rating to reflect their perception for each of the five sub-indicators, which can be found in the interactive graphics layout above. Each sub-indicator level is calculated as a relative value by dividing the positive percentage by the sum of the positive and negative percentages.
For instance, here is “Current Business Conditions” for the index measured in August, 2021.
Twenty-five percent (25%) said they had a “positive” view of current business conditions and 30.8% said they had a “negative” view. So, let’s do the math.
25 / 55.8 (25+30.8) = .448
That just means 44.8%. Get it?
Let’s also do the math for “Current Employment Conditions”. This month, 28.7% said they had a positive view and 39.3% indicated they had a “negative” view. Again, let’s do the math.
28.7 / 68 (28.7+39.3) = .422
That is 42.2%.
After we have all five sub-indicator levels, we can calculate the two subindex levels and ultimately the main index level.
Current Business Conditions: 44.8
Current Employment Conditions: 42.2
Expectations Business Conditions: 51.4
Expectations Employment Conditions: 54.2
Expectations Total Family Income: 50.2
The Present Situation Index is the average of the first two sub-indicator levels because they deal with views of the present situation, obviously. We did the prerequisite math above. The Expectations Index is the average of the last three sub-indicator levels because and measure the six-month outlook.
Remember “Order of Operations” in school? How about PEMDAS, or “Please Excuse My Dear Aunt Sally”?
1 – Parentheses
2 – Exponents and Roots
3 – Multiplication
4 – Division
5 – Addition
6 – Subtraction
We first deal with the parentheses before dividing to calculate each subindex level.
Present Situation Index (RED DASH)
(44.8 + 42.2) ÷ 2 = 43.5
Expectations Index (BLUE DASH)
(51.4 + 54.2 + 50.2) ÷ 3 = 51.9
Registered Voter Economic Confidence Index (GOLD SOLID)
(44.8 + 42.2 + 51.4 + 54.2 + 50.2) ÷ 5 = 48.6


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Session : Correlation Analysis and Independent Component Analysis
Nicholas Higham. Computing the Nearest Correlation Matrix - A Problem from Finance. Abstract Slides
Eric Moreau. Independent Component Analysis (Sources Separation) and Diagonalization. Abstract. Slides
Mohamed Hanafi. Global optimality of the successive MAXBET algorithm. Abstract Slides
Session : Triangular and QR factorisation
Per Christian Hansen. Computing Symmetric Rank-Revealing Decompositions via Triangular Factorization. Abstract. Slides
Patrick R. Amestoy, Symmetric minimum priority orderings for sparse unsymmetric factorization. Abstract. Slides
Cristian Gatu. Algorithms for computing the best subset regression models using the QR decomposition. Abstract. Slides
Petko Yanev. Computing the QR decomposition of a set of matrices with common columns. Abstract. Slides
Session : Regression models
Rasmus Bro. Jack-knife for estimation of standard errors and outlier detection in E.G. PARAFAC models. Abstract. Slides
Giorgio Tomasi. Fitting the PARAFAC model. Abstract. Slides
Paolo Foschi. A comparative study of algorithms for solving seemingly unrelated regressions models. Abstract. Slides
SVD and Least-squares computations
Lars Elde’n, PCR and PLS vs. TSVD and LSQR. AbstractSlides References
George Moustakides. SVD methods for CDMA communications. Abstract. Slides
Yann-Hervé De Roeck. Regularization of large least square problems in geophysics. Abstract. Slides
Jocelyne Erhel. Some inverse problems in electrocardiography. Abstract.Slides
Andy Nisbet. Hardware Acceleration of Applications Using FPGAs. AbstractSlides
Given a symmetric matrix what is the nearest correlation matrix, that is, the nearest symmetric positive semidefinite matrix with unit diagonal? This problem arises in the finance industry, where the correlations are between stocks. For distance measured in a weighted Frobenius norm we characterize the solution using convex analysis. We show how the modified alternating projections method can be used to compute the solution. In the finance application the original matrix has many zero or negative eigenvalues; we show that the nearest correlation matrix has correspondingly many zero eigenvalues and that this fact can be exploited in the computation.
In recent years, the independent component analysis problem and more
specifically the sources separation problem have received a lot of attentions
in the signal processing community because of their potential practical
interest. Numerous solutions have been proposed. Among them one can find
matrices (or tensors) joint-diagonalization based algorithms.
We first review the sources separation problem. Then we present the principle of many matrices joint-diagonalization algorithms in an unifying point of view. We also show some links of joint-diagonalization criteria with independence measure called contrast functions. We present some extensions to the joint-diagonalization of tensors. Finally some perspectives are given together with references.
The Maxbet method is an alternative to the method of generalized canonical correlation analysis and of generalized Procrustes analysis. Contrary to these methods, it does not maximize the inner products (covariances) between linear composites, but also takes their sums of squares (variances) into account. It is well-known that the Maxbet algorithm, which has been proven to converge monotonically, may converge to local maxima. The present paper discusses an eigenvalue criterion which is sufficient, but not necessary for global optimality. However, in two special cases, the eigenvalue criterion is shown to be necessary and sufficient for global optimality. The first case is when there are only two data sets involved; the second case is when the inner products between all variables involved are positive, regardless of the number of data sets.
We present a family of algorithms for computing symmetric rank-revealing VSV decompositions, based on triangular factorization of the matrix. The VSV decomposition consists of a middle symmetric matrix that reveals the numerical rank in having three blocks with small norm, plus an orthogonal matrix whose columns span approximations to the numerical range and null space. We show that for semi-definite matrices the VSV decomposition should be computed via the ULV decomposition, while for indefinite matrices it must be computed via a URV-like decomposition that involves hyperbolic rotations. Truncated VSV solutions are obtained by neglecting the small-norm blocks in the middle matrix. We compare these solutions with truncated SVD solutions, and give perturbation bounds for VSV solutions. Keywords: rank-revealing decompositions, matrix approximation, symmetric matrices, perturbation bounds
We introduce minimum priority ordering algorithms forsparse LU factorization where we assume that pivots can be chosen on the diagonal. All approaches based on a separate preordering phase traditionally involve the structure of A'+A to compute the sparsity ordering. But forming A'+A loses some information of A itself. Our ordering algorithms are based solely on the (unsymmetric) structure of A. Its efficient implementation requires us to extend the (symmetric) quotient graph model to the bipartite quotient graph. We will present the experimental results obtained on both multifrontal and supernodal approaches (MUMPS from Lyon-Toulouse and SuperLU from Berkeley) to show that with the new orderings we can better preserve the sparsity and exploit the asymmetry of the matrix.
Efficient parallel algorithms for computing all possible subset regression
models are proposed. The algorithms are based on the dropping columns method
that generates a regression tree. The properties of the tree are exploited
in order to provide an efficient load balancing which results in no inter-processor
communication. Theoretical measures of complexity suggest linear speed-up.
The parallel algorithms are extended to deal with the general linear and
seemingly unrelated regression models. Experimental results on a
shared memory machine are presented and analyzed.
A branch and bound algorithm which obtains the best models without investigating the whole regression tree that generates all possible subset models is proposed. The algorithm has the QR decomposition as a main computational tool and outperforms an existing branch and bound strategy based on inverse matrices. Computational results demonstrate the efficiency of the new algorithm.
The QR decomposition of a set of matrices which have common columns is investigated. The triangular factors of the QR decompositions are represented as nodes of a directed graph, where edges have weights. An edge between two nodes exists if and only if the columns of one of the matrices is a subset of the other. The weight of an edge denotes the computational complexity of deriving the triangular factor of the destination matrix from the triangular factor of the source node. Within this context the problem becomes equivalent to construct the graph and finding the minimum cost for visiting all the nodes. An algorithm which computes the QR decompositions by deriving the minimum spanning arborescence of the graph is proposed. Theoretical measures of complexity and numerical results from the implementation of this and alternative algorithms are derived and analysed.
In the last years multi-way analysis has become increasingly important because it has proved to be a valuable tool e.g. in interpreting data provided by current instrumental methods. PARAFAC is one of the most widely used multi-way models. But despite its usefulness in some real examples, up to date there is no available tool in the literature to estimate the standard errors associated with the parameter estimates. In this study we apply the so-called jack-knife technique to PARAFAC in order to find the associated standard errors to the parameter estimates from the PARAFAC model. The jack-knife technique is also shown to be useful for detecting outliers. A real example corresponding to fluorescence data (emission/excitation landscapes) is used to show the applicability of the method.
A multitude of different algorithms have been developed to fit a trilinear model to a three-way array. The aim of this study is to compare some of the available methods and to point out their limits and advantages. The algorithms considered in this paper are: GRAM-DTLD, PARAFAC-ALS, ASD, SWATLD, dGN (also referred to as Levenberg-Marquadt) and PMF3. These algorithms can be classified according to different criteria. One such classification is based on the "general" method they use to calculate the solution: GRAM is the only direct method, PARAFAC-ALS, ASD and SWATLD are based on the alternating least squares idea while dGN and PMF3 are derived from the Gauss-Newton method for the least squares problems. The algorithms and the underlying theories are exposed in general terms and two accessorial ethods, i.e. line search and compression, are illustrated when applied to the multiway case. In order to compare the algorithms, 720 sets of artificial data were generated varying features such as level and type of noise, collinearity of the factors and rank, and two PARAFAC models were fitted on each data set using the different methods: the first fitting the correct number of factors F and the second with F+1 components (the objective being to assess the sensibility of the different approaches to the over-factoring problem, i.e. when the number of extracted components exceeds the rank of the array). The algorithms have also been tested on two different real data sets constituted by fluorescence measurements again by extracting both the right and an exceeding number of factors. The evaluations are based on the number of iterations necessary to reach convergence, the number of operations per iteration, the time consumption, the quality of the solution and the amount of resources required for the calculations (mainly memory requirement) even though the last might be considered secondary.
There are several connections between certain methods for regression
analysis and numerical algorithms for solving ill-conditioned least squares
problems. In fact, principal component regression, PCR, is the same as
truncated singular value expansion, TSVD, and partial least squares, PLS,
is the same as Lanczos bidiagonalization (one implementation of which is
called LSQR). By considering so called filter factors, which relate PLS
to PCR, we demonstrate how PLS is capable of quickly reducing the least
squares residual at the same time as an approximation of the data matrix
is obtained. We will also show that similar residual reduction can be obtained
using principal components taken in an order determined by the right hand
Code Division Multiple Access (CDMA) is a technology applied to a number of important communications applications as mobile telephony, wireless networks and personal communciations. We present the theoretical modeling of this popular communication system, focusing on its main characteristic which consists in the simultaneous usage of the same communication channel by several users. This important advantage however, tends also to be its main handicap since it is the principal source of performance degradation. Indeed, it is clear that, to each user all other users play the role of interference. We therefore present popular signal processing algorithms that are used to combat multiuser interference. In particular we focus on adaptive methods, that rely on subspace tracking, which have a significantly better performance than their conventional least squares counterparts.
The processing of reflection seismic data in geophysics requires some very CPU-intensive computations. Prestack depth migration can namely be viewed, in the framework of waveform inversion, as a very large least square problem to be solved with much care about regularization issues. Although iterative methods are still preferred for their matrix-free implementations, direct methods might be tailored for this purpose. The application of both types of methods has been reviewed in our recent studies. A special attention is also paid to the deconvolution algorithm, as it provides a clear view about the difficult task of setting a threshold for the regularization parameters that should reach an optimal value depending on the noise level in the data.
The electrical activity generated by the heart propagates through the chest. Direct problems in electrocardiography aims at computing the potential at the surface of the torso, using a model of the electrical cardiac activity. For inverse problems, we consider a model where the cardiac activity is represented by the potential at the surface of the heart. The solution is then unique but not continuous. After a discretisation using either boundary element methods or finite element methods, we are faced to a discrete ill-posed problem. We formulate it as a general least-squares problem, which has to be regularized. We consider also time regularization, when a sequence of problems has to be solved.
High-level programming languages based on C, such as HandelC/SystemC can be used to program FPGA reconfigurable logic devices. In this talk we will present an overview of HandelC and discuss how it can be used to accelerate the execution of matrix and statistic applications. Single-precision floating-point arithmetic can be handled as fixed-point arithmetic, or by using the logarithmic arithmetic unit developed under the European Logarithmic Microprocessor, High Speed Logarithmic Arithmetic EU Long Term Research Project 33544. Current work at Trinity College has started into automatic conversion of C applications into HandelC/SystemC and the acceleration of lattice QCD and image segmentation applications using FPGAs.
In the framework of supervised learning, a methodology based on a combination of classification/prediction procedures is presented as a data mining tool enabling to extract information from complex and huge data sets for statistical purposes. This approach consists in a three stages data-driven procedure: tree-partitioning, modeling and model fusion. Main tools are represented by the tree production rules and nonlinear regression models. Particularly, in the first stage a recursive partitioning procedure is applied in order to find a suitable partitioning of the raw data into a relatively small number of internal homogeneous subgroups on which standard statistical modelling can be applied. Then, in each subgroup the dependence relation is described on the basis of the Generalized Additive-Multi-Mixture Models. This methodology, introduced by Conversano et al. (see reference), derives from a suitable combinations of different classifiers for statistical learning purposes. It results in a regression-like model defined upon a multiple combination of mixtures of models associated to the predictors, and has proven to be effective and feasible to capture the non-linearity structure of the data. At the end, in order to combine the results of the two previous stages, a final decision rules is formulated enabling to classify, or to predict, new instances. This methodology can be fruitfully applied for many data mining applications. Particularly, we focalize our attention to the analysis financial data, with particular emphasis on the identification of a productive asset allocation strategy in the framework of the management of financial portfolios.
Conversano, C. (2002). Regression Tree Criteria for Smoothing and Variable Selection in Generalized Additive Models: Modeling MIB30 Index Returns, Technical Report, Dept. of Mathematics and Statistics.
Conversano, C. (2002). Bagged Mixtures of Classifiers using Model Scoring Criteria, Technical Report, Dept. of Mathematics and Statistics.
Conversano, C., Mola, F. and Siciliano, R. (2001). Partitioning Algorithms and Combined Model Integration for Data Mining, Computational Statistics, 16: 323-339.
Conversano, C., Siciliano, R. and Mola, F. (2002). Generalized Additive Multi-Mixture Model for Data Mining, Computational Statistics and Data Analysis, 38/4:487-500.
The computational efficiency of various algorithms for solving Seemingly Unrelated Regressions (SUR) models is investigated. Some of the algorithms adapt known methods; others are new. The first transforms the SUR to an ordinary linear model and uses the QR decomposition to solve it. Three others employ the generalized QR decomposition to solve the SUR model formulated as a generalized linear least squares problem. Strategies to exploit the structure of the matrices involved are developed. The algorithms are reconsidered for the solution of the SUR model after it has been transformed to one of smaller dimensions.


This volume contains contributions illuminating much of the current research occurring in the area of visual perception. It encompasses all aspects of vision and its relationship to vehicle design, including both the internal and external design of the vehicle as well as the perceptual and cognitive limitations of the vehicle controller.
Issues specifically related to the vision of the driver are initially addressed and the problems of vehicle glazing and light transmission are considered. The major topics of visual perception and vehicle control are covered in three related chapters encompassing: collision avoidance, vehicle signalling systems and the acquisition of visual information. Moving on to the external environment and its relationship to vision, traffic signs are discussed. Approaches to the measurement and modelling of driver behaviour are dealt with and the area of telerobotic control of vehicles is considered. In-vehicle displays are covered in two related chapters addressing issues of visual workload and effects of display type.
It is hoped that the book, contributed to by experts from a diverse range of disciplines, including optometrists, psychologists, physiologists, human factors specialists and engineers, will stimulate the progression of research in this area, as effectively as the preceding volumes did.
This book is a very readable exposition of the modern theory of topological dynamics and presents diverse applications to such areas as ergodic theory, combinatorial number theory and differential equations. There are three parts: 1) The abstract theory of topological dynamics is discussed, including a comprehensive survey by Furstenburg and Glasner on the work and influence of R Ellis. Presented in book form for the first time are new topics in the theory of dynamical systems, such as weak almost-periodicity, hidden eigenvalues, a natural family of factors and topological analogues of ergodic decomposition. 2) The power of abstract techniques is demonstrated by giving a very wide range of applications to areas of ergodic theory, combinatorial number theory, random walks on groups and others. 3) Applications to non-autonomous linear differential equations are shown. Exposition on recent results about Floquet theory, bifurcation theory and Lyapanov exponents is given.
Food Wine Sleep Articles
Food Wine Sleep Books


- Castalia and
Philip Stook at U. Western Ontario
mentions an application of 3d convex hulls in mapping the surfaces
of these two asteroids.
- Convex hull,
Voronoi diagram, and Delaunay triangulation software
Nina Amenta's CG software directory.
- Convex hulls and interpolation. Ken Clarkson describes some implementation
details of algorithms for convex hulls, alpha shapes, Voronoi diagrams,
Processing and Pattern Recognition in Soil Structure. D. Luo of
Glasgow uses convex hulls and other geometric techniques to analyze
images of soil particles.
and tuberculosis diagnosis. Jason Everhart of Los
Alamos uses convex hulls as part of a heuristic for estimating the
percentage of lung volume occupied by a pneumonea infection.
This initial guess of the lung contour is then iteratively refined
to a more accurate representation.
Patent 4704694 uses convex hulls to recognize objects from video images.
Patent 5086482 seems to cover gift-wrapping methods of computing convex hulls in bitmap images.
Patent 5159645 performs character recognition by using convex hulls
to find the counters in each character. A similar idea also occurs in
- US Patents
5428717 cover methods for finding convex hulls of
polyhedra based on flipping reflex edges, along with an animated version
of this procedure that creates a smooth morph of the polyhedron to its hull.
Patent 5463721 describes the use of convex hulls in a method for finding a
path for a radiation-beam scanner so it can get enough data
to reconstruct object shapes. Patents
also use convex hulls for computerized tomography.
Patent 5465221 describes a part inspection system including the use
of convex hulls to determine stable orientations.
Patent 5483606 describes a method of registering (lining up) copied
pages with each other in a copying machine, using the convex hulls of
images of the pages.
Geometry in Action,
a collection of applications of computational geometry.
from a common source file.


Digital designers have to work within tighter constraints when it comes to creating a layout; they can't control the dimensions of the audience's monitor, after all. A common trick in web design is to use the golden ratio to divide space between the body of the website and the sidebar. Taking the measurements of the space they're working with, web designers can ensure that the body is 1.618 times larger than the sidebar by taking the total width of the canvas, dividing it by 1.618, and. The golden ratio is present throughout the world in design, the human body, nature, photography, art, and more. It seems to be nature's favorite equation. Actually, when you start looking for it, you might have a hard time un-seeing it. Here are some examples The Golden Ratio in Design The Golden ratio is another tool to help you deliver the right emotional and visual tone to the user. This theory exists whether you apply it intentionally or not — but what really matters is that you should understand and acknowledge it in an effort to create the most usable design possible Golden Ratio Designs is a small graphic and web design company based in New Damietta city - Egypt. We provide our services for clients from all over the world via email and phone. Here at Golden Ratio Designs, we are dedicated to personalized one-on-one service. If you have any questions at all, don't hesitate to contact us
The Golden Ratio is a mathematical ratio that's commonly found in nature. It can be used to create visually-pleasing, organic-looking compositions in your design projects or artwork. Whether you're a graphic designer, illustrator or digital artist, the Golden Ratio, also known as the Golden Mean, The Golden Section, or the Greek letter phi, can be used to bring harmony and structure to your projects Design and the golden ratio. Design basics · Graphic Design · Product design · Logo design · Photo composition · Photo cropping. Search GoldenNumber.net. Spam-free updates from the Phi Guy. Phi 1.618: The Golden Number. Dedicated to sharing the best information, research and user contributions on the Golden Ratio/Mean/Section, Divine Proportion, Fibonacci Sequence and Phi, 1.618. Connect. Golden Ratio Website Design Well-balanced content means creating pleasant compositions that relate to each other in beautiful proportions. Use the golden ratio to unite many components together in a harmonious way. For example, you can use it as a guideline for determining your website's dimensions Here are four ways to use the Golden Ratio in design: 1. Typography and defining hierarchy. The Golden Ratio can help you figure out what size font you should use for headers and body copy on a website, landing page, blog post, or even print campaign. Let's say your body copy is 12px. If you multiply 12 by 1.618, you'll get 19.416, meaning a header text size of 19px or 20px would follow the Golden Ratio and balance the 12px body font size
As mentioned in the introduction golden ratio and golden spiral are commonly used in graphic design as it makes a very easy way to create a harmonious and eye-pleasing design just by multiplying the size of a graphic element by 1.168 or by using the Golden Spiral to adjust the placement of the elements inside a graphic design layout When applied to graphic design, the Golden Ratio simply provides us with a way of creating harmony and proportion that our subconscious mind seems to be attracted to. As we've previously mentioned, the Parthenon and the painting of The Last Supper appear to use the ratio, as does the Apple logo, the Twitter logo and even natural forms such as ferns, flowers, sea shells and the human face. Yes, the Golden Ratio is everywhere In design, the Golden Ratio boils down to aesthetics— creating and appreciating a sense of beauty through harmony and proportion. When applied to design, the Golden Ratio provides a sense of artistry; an X-factor; a certain je ne sais quoi
Golden Ratio adds structure to design, which otherwise has an expressive nature. An easy hack of applying the golden ratio to any element is multiplying the size of the element by 1.618 for figuring out the size of another element or overlay the Golden Spiral for adjusting their placement. The golden ratio can be used for typography, images and much more The golden ratio is a mathematical ratio, found in many things both natural and designed, that dictates the most pleasing proportions of a shape or structure. The theory behind the Golden Ratio dates back historically to the time of Pi. The ratio has been used throughout history by philosophers, architects, and designers to create eye-catching, pleasing designs and structures. Some historical examples are the Parthenon in Greece, and the Pyramids in Egypt, where Architects leveraged this. Golden Ratio of Design can really save the day. But how to use it? At Imaginxp, we got you tips to please your audience The Golden Ratio is the number used when two quantities are divided in a way that their ratio is the same as the ratio of their sum to the larger one of the two quantities. That number is 1.618, also called Phi. Illustration using the golden ratio, by Vladanland The easiest way to demonstrate this is by using the Fibonacci Sequence
The Golden Ratio in Design. Web pages, ads, magazine covers, and illustrations all benefit from a layout that borrows from this ancient mathematical principle. The Golden Ratio can be used to guide the placement of objects, the shape of a logo, and more. Layout and Content, on the Web and Beyond . Let's start by looking at the role it plays in layout and content. In web design, the Golden. May 18, 2015 - Explore Valeo Mooha's board Golden ratio in design on Pinterest. See more ideas about Golden ratio, Golden ratio in design, Design
Golden ratio is used to find the right proportions that aesthetically pleases our eyes. Used to lead our reader's and user's eyes to certain points in the UI. A tool to help to place content and visual hierarchy. A mathematical sequence that has been used since the Greeks in their art and architecture Mathematically golden ratio is an irrational number, which means we can never achieve it perfectly in design; a debate going on forever. Takeaway for designers is, use of golden ratio is not something that will make or break your designs. Not every design composition can be derived using golden ratio
Golden ratio in design. Effective composition is a core part of a design. All the elements need to work together to maximize a pleasant experience. Moreover, each separate element, even the small one like an icon, has to be created in a harmony within itself. The golden ratio has a positive influence on visual perception, the reason why many graphic and UI designers apply it at their workflow. In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b > 0 Rightfully, the Golden Ratio sounds mystical because humans have been using the formula in their design for centuries. The best example is the Great Pyramid of Giza. However, there was never a mention of the proportion in the Rhind Papyrus until Euclid (365 B.C.-300 B.C.) first documented our consciousness of the ratio in his Elements. Plato theorized about it during the classical era Apple, Twitter, and Pepsi all use The Golden Ratio in the design of their brands. The Golden Ratio = visual equation for balance and perfection. Apple, Twitter, and Pepsi = avatars for balance and perfection. Here is an interesting visual representation of these brands' pursuit of perfection, courtesy of Behance: Twitter and Apple's logo use is sufficiently complex. But through this visual.
The Golden Ratio is a design concept based on using the Fibonacci sequence to create visually appealing proportions in art, architecture, and graphic design. The proportion, size and placement of one element compared to another creates a sense of harmony that our subconscious mind is attracted to. To use or not to us We use the golden ratio widely in web and app design. In particular, it's very easy to incorporate when building wireframes. You can ensure that the content you need is prioritized properly and that the aesthetic demands of the layout will be met without doing too much design work at first. Only when you, for instance, decide where you will place elements and features over this framework. First studied in ancient Greece and Rome 2,500 years ago, the Golden Ratio (sometimes called the Golden Number or the Golden Mean), is an equation for scale and proportion. The number is, roughly, 1.618. The ratio is, again roughly, 60/40. (If you want the exact numbers, feel free to Google the Golden Ratio The golden ratio is a ratio found in nature that somehow makes an object aesthetically appealing. Artists throughout history such as Salvador Dali and Leonardo Da Vinci attempted to create works based on this proportion in order to make them look beautiful. This ratio has also been applied into architecture for centuries, such as the Great Pyramid of Giza The Golden Ratio and Website Design. Whether you're into math or your head's about to explode, the Golden Ratio is a bit easier to understand in terms of design. You've done the heavy lifting. Now it's time to take the basic overlay and make your web components perfectly pleasing. The Golden Ratio and Layout . If you want a perfect Golden Ratio layout, set the dimensions to 1:1.618.
Similar to using a grid in layout design, using the Golden Ratio provides a framework for my design decisions. Granted, you can't superficially use the Golden Ratio and think everything will always be perfect. Using these proportions in your design work will take time and practice. But the more you use it, the more you will start to see relationships between elements of your design and begin to spot and correct areas that are inconsistent in your work and just don't feel right Golden Ratio in Setting Layout Dimensions Layout, which is used for arranging the visual elements on a page in web or graphic designing. It consists of organizing the art composition to achieve specific communication objectives. In this genre, the golden ratio is used to define the width of the panels, sidebars or even height of the views Professor Keith Devlin shows the beauty created by the Golden Ratio in design. Devlin is quoted saying that there's No evidence that things conforming to this ratio are more beautiful. In his own video lectures though he describes the unique impact of the golden ratio in the beauty of fractal patterns, as shown below Here are three tips for using the golden ratio in design projects. Use the ratio to create a base website grid for the main content area and sidebar. According to W3Schools, the most common browser resolution at the start of 2018 is 1366 by 768 pixels. Apply the golden ratio for a content area of 846 pixels wide with a sidebar that 520 pixels wide. When considering the ratio for this purpose.
The Golden Ratio and Notre Dame Phi and the use of the golden ratio are found in the design of Notre Dame in Paris, France. The Gothic Cathedral was built beginning in the year 1163, and completed in the year 1345. Claimed as the first Christian church in Paris, Notre Name was built upon the Roman temple of Jupiter The golden ratio is the ratio of approximately 1 to 1.618. These are extremely important numbers to mathematicians. But what do they mean to us artists? Well there have been studies which suggest designs set out using the golden ratio are aethetically pleasing. We can use the golden ratio to help design our paintings and position our subjects
The Golden Ratio in Design Web pages, ads, magazine covers, and illustrations all benefit from a layout that borrows from this ancient mathematical principle. The Golden Ratio can be used to guide the placement of objects, the shape of a logo, and more. Layout and Content, on the Web and Beyon The golden ratio is a mathematical proportion between the elements of different sizes which is thought to be the most aesthetically pleasing for human eyes. The golden ratio equals 1:1.618 and it is often illustrated with seashell-shaped spirals which you could have probably seen on the Internet
May 9, 2012 - Golden Ratio by Josh Smith from Tattly Temporary Tattoos. Quality, non-toxic and made in the USA. Fake tattoos by real artists The square root of 5 is approximately 2.236068, so the Golden Ratio is approximately 0.5 + 2.236068/2 = 1.618034. This is an easy way to calculate it when you need it. Interesting fact: the Golden Ratio is also equal to 2 × sin (54°), get your calculator and check Each application of the golden ratio is different and unique, but each adds to its overall architectural beauty and harmony with the design principles found in nature. Other famous applications of the golden ratio in architecture include the CNN Tower in Canada, the works of Frank Lloyd Wright and Le Corbussier. It is commonly used in modern architecture as well Golden Ratio design, Hanoï. 26 527 mentions J'aime · 41 en parlent · 14 personnes étaient ici. Thiết kế,thi công nội ngoại thất và cung cấp thiết bị liên..
How designers can use the Golden Ratio in their design. Let's take a look at the ways designers can use this magical ratio when designing. Balance your layout's structure and form . First, to figure out just what the Golden Ratio is you can use a Golden Ratio calculator. This will give you the 1:1.61 ratio you're looking for so you can easily create the a document in Illustrator, Sketch. Introduction The golden ratio also is called the golden mean or golden section. Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which may be cut into a square and a smaller rectangle with the same aspect ratio
Golden Ratio in Design. Effective composition is a core part of a design and all the elements need to work in harmony to maximize a pleasant experience. Moreover, each separate element, even as small as an icon, has to be created in perfect harmony within itself. The Golden Ratio has a positive influence on the visual perception which is the reason why many graphic and UI designers apply it at. Multiply a font size or a design element by the Golden Ratio, and you're one step closer to see your layout start coming together. Or you can always overlay the Golden Spiral as a handy guide. Because of the scientific, even universal nature of the Golden Ratio, designers often use it whether they know it or not. However, it's always good to check to see if your designs sit within the. Golden ratio is a design consultation company, a collectively owned and operated LLC with a fully insured and licensed contracting team with over 50 years of combined experience. We specialize in everything from earth building techniques to large scale construction, fine woodworking craftsmanship to permaculture design
Golden ratio logo designers in India as well the other counties use the theory of golden ratio in designing various logos of their clients. Everytime they draw the figure and observe, they find out a new design. It also helps in maintaining the authenticity of the logo of a particular company by not letting a chance for others to plagiarise or infringe the acts of trademarks The Design version is great for creative types who prefer a simple user interface to access golden ratio grids, diagonals and spirals. PhiMatrix has a completely-redesigned, streamlined user interface to make composition and design quick, simple, intuitive and fun. It is recommended for artists, designers and photographers. Includes all the best and most commonly used templates and features.
. This ratio is proven to be aesthetically pleasing to the human eye. It creates a sense of visual balance, harmony and beauty in the designs we find in nature. Artist and designers alike apply this. GOLDEN RATIO IN WEB DESIGN: TOOLS . Phi Calculator - great tool to know golden ratio dimensions. You just need to enter any number into this tool and it will give you the result you need for the golden ratio. It's free and very easy to use. UX triggers - awesome tool to test any website according to golden ratio perfection. This tool.
<p>They all have one simple concept in common.The Ancient Greeks were one of the first to discover a way to harness the beautiful asymmetry found in plants, animals, insects and other natural structures. It has been thought that early Egyptians used it to construct the pyramids of Giza. Proper use of the golden shapes can harness a proper balance and can turn a good design to a great one. The golden ratio is a mathematical ratio, found in many things both natural and designed, that dictates the most pleasing proportions of a shape or structure. The theory behind the Golden Ratio.. The Golden Ratio Defined The golden ratio describes the perfectly symmetrical relationship between two proportions. It is defined as 1:1.618033987 and is represented by the Greek symbol Phi. In other words, this means that if length A is 100px, then length B would be 161.80px The golden ratio is especially used in web design. When you are creating a blog layout, it is typical to create a layout where the content is the larger portion of the golden grid, and the smaller part is the sidebar. Even Design Crawl is following the general layout of the golden ratio, which you can see in the example below. Keep in mind, when a site is responsive, it may not be the exact same on every monitor. It's consistent, but not an exact match Golden Ratio in Graphic Design: Golden Ratio adds structure to design, which otherwise has an expressive nature. An easy hack of applying the golden ratio to any element is multiplying the size of the element by 1.618 for figuring out the size of another element or overlay the Golden Spiral for adjusting their placement
Simply, the golden ratio (also called the golden rectangle and golden mean) is a shape with a proportion of 1 to 1.618. More complexly, the math can be described like this as explained by the Interaction Design Foundation:. Each number in the Fibonacci sequence is simply the sum of the two numbers before it Golden Ratio is of great importance in the design of architecture, appliances, logos and photos. I don't want to write about it a lot, you can learn it in Wikipedia. I will say briefly: our consciousness tends to harmony and beauty, and the golden ratio is the elegant way to make a product more comfortable and nice for perception. Simply put, it's a tool to strike a balance in the design
14+ Golden Ratio in Design Easy Way Golden Ratio has been a common context in art and architecture since time immemorial. Based on famous Fibonacci sequence, this mathematical equation is found in many iconic architectures and art forms as well as around the nature The Greek sculptor Phidias, (ca. 490-430 BC), made extensive use of the golden ratio in his works. The structures of the Roman classical era are said to be designed within the Golden Ratio. The Egyptians, who made extensive use of it in the building of temples and pyramids, called it the sacred ratio For centuries, designers have used the golden rectangle in garden design, sometimes without even realizing it. If you're wondering how this could be, take a look at your own garden. How many groups of 3, 5 and 8 do you see? You planted them that way because you found a grouping that size visually appealing without knowing that groups of this size are an integral part of the golden ratio. Man
The golden ratio is frequently used in photography, design, and architecture. It helps you build a balanced composition and establish a strong focal point . It isn't easy to use an irrational number in creative fields, but there are tools and methods that can ease the work for you The golden ratio's aesthetic bona fides are an urban legend, a myth, a design unicorn. Many designers don't use it, and if they do, they vastly discount its importance. There's also no. The golden ratio is when we divide a line into two parts; one long and the other short. The idea is to ensure that the entire line's length when divided by the longer part, is equal to the longer part when divided by the shorter part. The diagram shown below will hopefully give you a better answer What the Golden Ratio Looks Like . The easiest way to picture the Golden Ratio is by looking at a rectangle with a width of 1, and a length of 1.168... If you were to draw a line in this plane so that one square and one rectangle resulted, the square's sides would have a ratio of 1:1. And the leftover rectangle? It would be exactly proportionate to the original rectangle: 1:1.618 Our Golden Ratio design is made from quotations about the connection between math & nature and in the shape of a Golden Spiral and Golden Rectangle. The Golden Ratio, a.k.a Phi (represented by the Greek symbol Φ), a.k.a the Golden Mean, a.k.a the Golden Section, is woven throughout so many aspects of our human existence and the universe we live in. And yet we are mostly oblivious to its power over our subconscious. This power attracts us like moths to a light except in this analogy the.
. See more ideas about golden ratio, fibonacci, sacred geometry Golden Ratio in Web Design. When mathematics and beauty are put on a designer's palate, what results is a true masterpiece. Web pages, ads, magazines, etc. almost everything seems to borrow the aesthetics from this magical ratio. Designers have been using the same as a guide for making proper use of the web-space and the placement of objects e.g. the shape of a logo, etc. Web Layout and Web. Creating a Golden Rectangle is pretty straightforward, and starts with a basic square. Follow the steps below to create your own Golden Ratio The Golden Ratio is a mathematical ratio discovered and commonly found in nature, which is now visible almost everywhere like in architecture, music, paintings, modern design etc. When used effectively, it creates designs that are naturally and aesthetically appealing to the eye by way of their composition Examples of Golden Ratio in Design Logos. Golden Ratio is widely used in logos. In the following examples the text or the dimensions are apparently based on proportions of the golden ratio. Credit Cards. If we measure the sides of our credit or debit cards, we will notice that the relationship between their sides is. the golden number. When the credits card were designed, they thought of.
Golden Ratio in Nature by Mate Marschalko via medium. How to use the Golden Ratio in graphic design — One of the best things about the Golden Ratio is that it gives you a simple number to help structure the otherwise expressive nature of design. Simply multiply an element's size by 1.618 to figure out the size of another element, or overlay. Nov 5, 2020 - Explore Jim Slagle's board Golden Ratio in Design, followed by 178 people on Pinterest. See more ideas about golden ratio in design, design, golden ratio The golden ratio is a ratio that you use to divide a rectangle into a square, and the ratio is 1:1.61, and that will form two columns: one square; and one rectangle. If you repeat the process and rotate it at the same time, you'll end up with an infinite spiral like this


A computational model of learning to count in a multimodal, interactive environment
- Silvester Sabathiel, Department of Computer Science, NTNU Trondheim, Trondheim, Norway
- Jay McClelland, Stanford University, Stanford, California, United States
- Trygve Solstad, Department of Teacher Education, Norwegian University of Science and Technology, Trondheim, Norway
AbstractWhen learning to count, children actively engage with a variety of counting tasks and observe demonstrations by more knowledgeable others. We investigate how a single neural network-based agent, situated in a multimodal learning environment, can learn from observing such demonstrations to perform multiple number tasks such as counting temporally and spatially distributed objects, and a variant of the ‘give-N’ task. We find that i. the agent can learn different tasks that require counting, ii. learning progresses in similar stages for different tasks, iii. sequential learning of subtasks aids learning of the full counting task, and iv. a mechanism for updating memory when each object is counted emerges from learning the task. The work relies on generic deep learning processes in widely used neural network modules rather than mechanisms specialized for mathematics learning, and provides an architecture in which a sense of number emerges from learning several different number related tasks.
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So I was live-plotting some results from a simulation code (written in C), which was producing results for an input parameter (in this case Temperature), over a range generated by a for loop. Pretty standard computational physics. It was clearly suboptimal watching the new dataset arrive in small, fine, increments from zero upwards; the obvious thing was to change the discretisation of the for loop & make it more coarse. Yet, surely there is some way to get better coverage of the dataset, like a ‘streaming’ JPEG or GIF arriving with increasing discretisations of the blockiness?
What about some mathematical function that would jump around the space with good coverage? A pseudo-random number generator with a fixed period? Some mathematical function that would map an ascending series of integers into spatial coverage? Modulus arithmetic on some prime or co-prome addition?
How about reversing the binary digits in an incrementing integer? So instead of going 0,1,2,3…254,255; you would bounce around the number line: 0,128,64,192,32,160 … 127,255. So it’s sort of doing a binary split of the unoccupied locations on the number line at each step. You get maximum coverage, with increasing levels of fidelity, ending up with a complete (but missorted) dataset.
So with a Bit Twiddling hack found via Stackoverflow (http://graphics.stanford.edu/~seander/bithacks.html#ReverseByteWith64BitsDiv), the totally crazy bit-shifting code (for a byte, so covering 256 values) looks like: https://gist.github.com/jarvist/368622717a5d3bcadfc0
It’s pretty low level (in Python or similar, you could reorder a list, and iterate over that instead), but the result is nice! It’s almost so useful that perhaps one should write it into a mini function or macro…


27 June 2014
Hopes are high for 49 students from 20 different African countries who graduated with a master’s degree in Mathematics in Cape Town this week. The students – from countries including Egypt, Ethiopia, Ghana, Kenya, Nigeria, Rwanda and South Africa – completed their studies at the African Institute for Mathematical Sciences (AIMS) located in Muizenberg.
Former South African president Kgalema Mothlanthe attended the ceremony on 25 June.
“No modern society progressed without Maths as a driving impulse … South Africa, Africa and the rest of the world looks forward to your contribution. I hope that you will put this highly privileged knowledge at the service of society,” Mothlanthe told graduates.
“Students who do exceptionally well in Mathematics and natural sciences are the brain power [of society]. Innovation and invention is their domain. If we hope to take Africa higher we need more mathematicians and scientists.”
AIMS director Barry Green said their intention was that the “flame for mathematics has to be ignited in the young … This is what we do at AIMS … to create a new future for Africa,” he said.
Students travel on scholarship from various parts of the continent and are housed in Cape Town throughout their studies. They study with partner institutions, including the University of the Western Cape, University of Cape Town and the University of Stellenbosch.
Horace Ekete from the Democratic Republic of Congo (DRC) completed a degree in computer science before traveling to Cape Town. She said she planned to return to the city to further her studies.
“For now, I will go back to my country. I am a computer scientist and want to continue with my academic career. But we don’t have this quality of education in DRC,” said Ekete.
She said, when she started the master’s degree, she did not “even know the importance of mathematics … It was not easy to believe that mathematics can help for the development of country. Mathematics is everywhere,” said Ekete.
“You could have a problem related to health or the economy and we can apply mathematics models to solve the problem.”
“We learn about mathematics models. You could have a problem related to health or the economy and we can apply mathematics models to solve the problem.”
Saga Abdalla from Sudan completed a degree in physics before embarking on her master’s degree in mathematics.
She said of AIMS: “This programme can change Africa. It is a key to go to other places … After I came to AIMS, I applied for the Italian scholarship. I think they selected me because of AIMS because we have good professors.”
Abdalla said it was the first time she traveled to a foreign country where Arabic was not widely spoken.
“It was strange because there were so many people speaking different languages. The advantage of living with many people is that you can understand different people,” she said.
Abdalla intends to “work in Sudan and transfer what I have learned”.
“The education system in Sudan can improve. I see myself playing a role in that,” she said.
Fanuel Otieno from Kenya will return to his country to do an internship with a statistics centre.
“I’ll be doing data analysis specifically linked to farming and agriculture,” he said.
His goal is to ultimately “be a top, professional statistician who consults with Kenyan organisations in solving their statistical problems”.
“The master’s course has increased my mathematical knowledge. We are able to see how we can apply mathematics to solve problems in everyday life,” said Otieno.
“I feel very independent now. I can do research on my own.”
Otieno said the teaching method at AIMS differed from his studies in Kenya.
“In Kenya, the institutions are exam and assessment oriented. At AIMS we do assignments, and you are encouraged to spend time researching,” he said.
“When you do the assignment you have a broad understanding of what you have learned.”
AIMS describes itself as a “pan-African network of centres of excellence for postgraduate education, research and outreach in the mathematical sciences”.
It is a partnership between six universities: UWC, UCT, Stellenbosch University, Cambridge University, Oxford University and the University of Paris-Suid. It was established in 2003 and hundreds of students have lived at its Cape Town main building since then.


In the Sixth Form students continue to work towards qualifications in Food Tech, ICT, Maths and English at their appropriate level. To ensure they reach their full potential, students are taught in small groups with individualised levels of support. Maths and English classes are made up of mixed KS4 and KS5 students to ensure progress is made across all abilities.
A summary for the sixth form curriculum pathway is given in the table below.
|Core Subjects||Number of lessons||Accreditation|
|English||4||ELC 1-3 or Level 1/2|
|Maths||4||ELC or Level 1 or 2 GSCE (where appropriate)|
|Cooking||2||BTEC Level 1 and 2|


A team of Italian scientists have found a way to change their impressively complex twisted shape. chaos theory According to the actual jewelry new paper Published in Chaos magazine. These works are not simply inspired by chaos theory. They were created directly from that mathematical principle.
“It was a great joy for the whole team to see the chaotic shapes transform into real, sophisticated, lustrous, physical jewellery. , was very exciting.” Co-author Eleonora Bilotta said of the University of Calabria. “We think of it as the same joy a scientist feels when his theory takes shape, or an artist when he finishes a painting.”
The concept of chaos may suggest complete randomness, but to scientists, the system’s output appears random because it is so sensitive to initial conditions that it obscures the underlying rules of internal order. It means the system that is For example, stock markets, rioting crowds, brain waves during epileptic seizures. , or the weather. In a chaotic system, small effects are amplified by repeated repetitions until the system becomes critical. The roots of today’s chaos theory are accidental discovery Mathematician turned meteorologist in the 1960s Edward Lorenz.
Lorenz saw the advent of computers as an opportunity to combine mathematics and meteorology to improve weather forecasting. He set out to build a mathematical model of weather using a set of differential equations that describe changes in temperature, pressure, wind speed, and more. Skeleton Once his system was complete, he kept running simulations continuously on his computer. This will generate a day’s worth of virtual weather every minute. The resulting data resembled naturally occurring weather patterns. The same thing never happened to him twice, but there was clearly an underlying order.
One winter day in early 1961, Lorenz decided to take a shortcut. Instead of starting the whole thing over again, he started halfway through and entered the numbers directly from the previous print to give the machine an initial state. Then he walked down the hallway to drink coffee. When he returned an hour later, he found that the new printout, rather than replicating the previous run exactly, had changed the virtual weather significantly from its previous pattern. found that within hypothetical “months” all similarities between the two were lost. Had disappeared.
Computer memory stored 6 decimal places. Only three are shown to save space on the printout. Lorentz argues that a difference of 1 in 1000 is negligible, and that shorter rounded numbers are assumed to be similar to small winds that are unlikely to significantly affect large-scale weather features. entered.But For certain systems of Lorenz equations, such small fluctuations turned out to be catastrophic.
This is known as sensitive dependence on initial conditions. Lorenz then described his findings as “butterfly effect: The nonlinear equations that govern weather are incredibly sensitive to initial conditions. A flapping butterfly in Brazil could theoretically cause a tornado in Texas. Metaphors are especially apt. For further investigation, Lorenz simplified his complex weather model to focus on rotating fluid convection in the atmosphere. It’s basically a gas in a solid rectangular box that has a heat source at the bottom and is cooled from above, with warm air rising up and cold air sinking down. He simplified some hydrodynamic equations and found that plotting the results for specific parameter values in his three dimensions produced unusual butterfly-shaped figures.


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Green Island offers a pre-K through grade 12 academic program. Students continually build on their skills each year. The district's educational programs align to ensure ensure that every child will graduate prepared for college, career and citizenship, along with the New York State Department of Education’s learning standards.
Heatly Elementary School
The Heatly Elementary School academic program includes grades K-6 and builds on the foundational skills students acquire during the primary grades and provides them with academic challenges while taking into account individual student learning needs.
Heatly Junior High School
The Heatly Junior High School academic program includes grades 7 and 8 and builds on the skills learned duing the primary grades, while preparing students for high school. Students complete coursework in the core subjects of math, English, social studies and science, as well as art, music, physical education, health and Spanish.
Heatly Senior High School
The Heatly Senior High School academic program includes grades 9-12 and is the culminating period of a students' time at Heatly. In addition to the core subjects, students are exposed to a variety of subjects to help better prepare them for life after high school - whether it be attending college, entering the workforce or enlisting in the armed forces.
Next Generation Learning Standards
The Board of Regents adopted the newly revised English Language Arts and Mathematics Learning Standards on September 11, 2017. The new standards have been the result of over two years of collaborative work to ensure New York State has the best learning standards for our students. Over 130 educators and parents worked together to make recommendations and revise the standards, resulting in a new set of revised English Language Arts and Mathematics Learning Standards.


Physical and Mathematical Model of Heart and Cardiovascular System
The cardiovascular system is modelled as a fluid flow system consisting of networks of pumps and piping systems. A mathematical model relating different cardiovascular parameters was developed. The change in cardiovascular parameters with individuals’ physical activity level, habits and environmental factors was established. The models used to predict how an individual can control the cardiovascular parameters to be healthy and diagnosing problems in the system.Keywords: Blood Pressure; Circulatory system modelling; Heart Rate.
Copyright (c) 2020 Aditya Kundu, Ananya Kundu, Goutam Kumar Kundu
International Journal of Current Research in Physiology and Pharmacology; Volume 4, Issue 2; 2020; 4-10


All right reserved. No part of this work may be reproduced in any form or by any electronic or mechanical means, including information storage and retrieval system, without permission in writing from the Organisation.
The ____________ of a given number is that number which when multiplied by itself gives a product equal to the given number.
In Hexadecimal System, C is representing ____________
Another name for bicimal is ____________
A sequence in which each term is formed by multiplying the preceding term by a constant is the ____________
If log 36.74= 1.5652, the underlined number is called ____________
A ____________ is an equation of the form ax2+bx+c=0, where a, b and c are constant and a≠0.
____________ is the reverse of Differentiation.
b2-4ac is called ____________
Error X 100 is called ____________ Actual Measurement 1
In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares of the other two sides and vice-versa is called ____________
A quadratic of the form (x+p)2 is called a ____________
Consider the formula for the volume of a cone V= 1/3πr2h. In this case, the volume is a function of two variables, r and h. the volume varies directly as the square of radius and as the height. This is called ____________ Variation.
An expression in which highest power of the unknown is 1 is called ____________
____________ is a sequence in which the difference between any term is constant.
If a>0, the parabola y=ax2+bx+c faces upward and has a ____________ point.
A ____________ is a rectangular array of numbers that are enclosed within brackets.
The relationship between two variables in which their product remains constant is called ____________
A number written in the form A x 10n where 0<A<10 and n an integer is said to be in ____________
The transpose of the matrix of cofactors of the matrix A is called____________
A matrix in which the number of rows equal number of columns is called ____________ Matrix.
The x-coordinate of any given point on the graph is called ____________
The ____________ states that if a polynomial function f(x) is divided by x-a, we obtain a quotient Q(x), and the remainder is F(a).
A cubic equation has ____________ roots.
Expression which contain two terms such as 3a+2c, 16x-4x2 are called ____________
The ____________ of a number to a certain base is the power to which the base must be raised to obtain the number.
The ____________ of two sets A and B, written as AnB, consists of elements which belong to both A and B.
A pyramid is a solid with a polygon base which meets to a common point called the ____________
A statement which compares two expressions which are not equal is called ____________
A number whose square root cannot be expressed as a fraction or a quotient of two integers is called a ____________
An algebraic expression that contains only one term such as 3x, 8y2, 15y are called ____________
A ____________ is a general name for any group or collection of distinct elements.
Half of a diameter is called ____________
If 00<θ<900 and θ is in the first quadrant, all the trigonometrical ratios are ____________
Circles and rectangles which are representations of sets are called ____________
If a pyramid, standing on a horizontal flat surface is cut through parallel to the flat surface, the top part is a smaller pyramid and the remaining part is called a ____________
Another name for Empty set is ____________
The ____________ states that is x-a is a factor of the polynomial function F(x) then F(a)=0
A ____________ of a circle is a portion enclosed by two radii and an arc of the circle.
A ____________ illustrates pictorially the relationship between two variables.
The values of x that satisfy the quadratic equation are called the ____________ of the equation.
Range is classified into two ____________ and ____________
____________ are formed at the point of intersection of two lines.
Each angle in a square or a rectangle is ____________
If the standard deviation is S and the mean is Ẍ, the relative dispersion which is also called the coefficient of dispersion or ____________
A ____________ is the straight line, curve or traced by a moving point P.
The perimeter of a segment is calculated by ____________
The latitude of the equator is ____________
____________ is a triangle in which there are no equal sides.
The values of X that satisfy the quadratic equation are called the ____________ of the equation.
The average of the sum of the deviations of the observations from the mean where all the deviations are taken as positive is called the ____________
A ____________ is an angle that is greater than 1800 but less than 3600.
Payments to sales people are called ____________
The ____________ is a positional average.
____________ is the distance round the boundary of a closed plane figure.
Data which is not organized and presented in a definite order of magnitude is called ____________
The points where the straight line cuts the X and Y axes are called ____________
When the cumulative frequencies are plotted against corresponding upper class boundaries the line graph obtained is called the ____________
The set S of all possible outcomes or equiprobable outcomes of a given experiment is called a ____________
The ____________ of a place on the earth’s surface is the angular displacement in degrees north or south of the equator.
A ____________ is a figure bounded by three straight lines.
The ____________ is determined by observation and not by calculation, considering only the frequency of occurrence of the modal observation.
The measure of dispersion which is obtained by computing the root mean square of the deviations from the mean is called ____________
The sum of the exterior angles of any polygon is ____________
The bisector of an angle of a triangle that divides the opposite side is the ratio of the sides containing the angles. The above is called ____________ theorem.
A tabular arrangement of numerical data by classes, together with corresponding classes frequencies is called ____________
When the angle of a minor sector is θ0, the angle of corresponding major sector is ____________
The sum of the principal and the interest is called ____________
If the product of any two numbers equals 1, then the two numbers are called ____________ of each other.
When two or more triangles are equal in all respects, they are said to be ____________
A four-sided closed figure is called a ____________
If a, b and c are three consecutive terms of an A.P, then b is the ____________ of a and c.
If the maximum value of sinθ is 1, i.e when θ = 900, the maximum value is ____________
If we know the values of α+β and αβ for a given equation, we can calculate the values of other functions of α and β, provided they are ____________
Near 900 and 2700 tanθ increases very rapidly and the curve approaches the vertical lines through 900 and 2700 on each side but never actually touches these lines. Such lines are called ____________ to the curve.
The sum of first 45 natural numbers are ____________
If a, b, c are consecutive terms of a G.P, then b is the ____________ of a and c.
N tends to infinity can be denoted as ____________
If a>b, then ax < bx and a/x < b/x if x is ____________
The centre of gravity of a triangle is called ____________
The point where the three medians of a triangle meet is called ____________
The notation ꞁxꞁ means the modulus or ____________ of x.
Write 10,500,300,000,000,000 in words ____________________________________________________
Write MCMIX in ordinary numeral. ________________________________________________
The angle subtended at the circumference is twice the angle of the centre subtended by the same arc. YES/NO____________
Angles in the same segment of a circle are not always equal. YES/NO ____________
A tangent to a circle is perpendicular to the radius drawn from the point of contact. YES/NO ____________
The angle between a tangent and a chord drawn from the point of contact is equal to any angle in the alternate segment. YES/NO ____________
The two tangents drawn from an external point to a circle are not the same length. YES/NO ____________
A quadrilateral is cyclic, if and only if the sum of each pair of opposite angles is right angle. YES/NO ____________
If AB and CD are two chords of a circle which cut at a point P (which may be inside or outside a circle) then, PA.PB=PC.PD. YES/NO ____________
If P is a point outside a circle and T, A, B are points on the circle such that PT is a tangent and PAB is a secant then PT2=PA.PB. YES/NO ____________
A segment of a circle is the part of the plane bounded by an arc and its chord. YES/NO ____________
The angle subtended by a diameter at the circumference is equal to two right angles. YES/NO __________
Polynomials = Quotient X Divisor + ____________
The ____________ of conjugate surds is not a surd.
If D is negative (D<0 or b2<4ac), then there is no real value for √D. The equation has ____________ roots.
A B C From this figure, the points A, B and C are said to be _________
The three altitudes intersect in a simple point is called _________
The algebraic procedure of calculating the derivatives is called _________
The derivation of a function is the slope or _________ of the curve at any given point.
A point on a curve at which dy/dx = 0 is called a _________
In integration, the function to be integrated is called the _________
A solid which has a central axis of symmetry is a solid of _________
Acute triangles only have two angles acute. YES/NO ____________
Quadrilaterals are also sometimes called tetragons. YES/NO ____________
All squares belong to the rhombus family. YES/NO ____________
Some parallelograms have lines of symmetry depending on whether they are also squares, rectangles of rhombuses but most do not. YES/NO ____________
Convex shapes have at least one reflex angle. YES/NO ____________
Irregular shapes are always concave. YES/NO ____________
Ellipse is like circle which have 2 lines of symmetry. YES/NO ____________
The perimeter of crescents is made from three circular arcs. YES/NO ____________
Cuboid is an example of 3D shapes. YES/NO ____________
____________ is a shape with 20 faces, 30 edges and 12 vertices.
If two integers a and b have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1, they are said to be ____________
The set of numbers denoted by Q is called ____________
The name of one term of a sequence which we can use the relation again and again to find the other terms is called ____________
If D=b2 – 4ac is a perfect square, the roots will be ____________ numbers.
The method of differentiating composite functions is called the ____________.
Another name for the maximum and minimum points of a curve is called ____________
The result of an integration is called ____________
∫F(x)dx is called ____________
A and B are ____________ events if either A or B must happen.
Another name for central tendency is called ____________
This shape is called ____________
____________ is a mathematical information organized in columns and rows.
____________ is the branch of Mathematics that deals with the collection, organization and interpretation of data.
____________ is a measure of the spread or dispersion of a set of data.
____________ is the degree of asymmetry of a distribution.
____________ is the likelihood that a particular event will occur expressed as a percentage between 0 and 100%.
____________ is the entire set of items from which data can be selected.
____________ is another name for circle graph.
____________ is the probability of an event as determined by comparing the areas (or perimeters, angle measures etc) of the regions of success of an event to the total area of the figure (sample space).
A ____________ is defined as coin where the probability of landing heads up or tails up are the same (0.5).
The processes in which there are an observable set of outcomes are called ____________
____________ is a subset of the sample space.
Let A and B be two events. The probability that A will occur given that B has already occurred is the ____________ of A given B and is denoted by P(A\B).
____________ is the number of ways of picking K unordered outcomes from n possibilities.
____________ Theorem states that, if two angles of a triangle are congruent, the sides opposite these angles are congruent.
The ____________ of a number x to the given base b is the power to which b will be raised such that it equals x.
If Sn=a+(a+d)+(a+2d)+…………+[a+(n-1)d], this expression is called ____________
A mother told her daughter, “I was as old as you are at present at the time of your birth”. If the mother’s present age is 38years. What is the present age of the daughter? ____________
If b2-4ac=0, the two roots α and β are real and ____________
The function f:x→1/x where x≠0 is called ____________ function
In a farewell party, each student paid as much amount in naira as the number of students. If the teacher’s contribution is N200 and the total collection is 1,100. The number of the students in the farewell party is ____________
A square matrix A is said to be ____________ if AAT=I
A ____________ of the plane is a one-to-one mapping from the set of points in the plane onto itself.
The HCF of the two numbers is 68 and their LCM is 2142. If one of the numbers is 204, find the other number. ____________
The derivative of cosec x is ____________
A ____________ equation is an equation which involves at least one derivative of an unknown function.
Gbonjubola secured 40% marks in Geography, 30% in English and 80% in Mathematics. If the maximum marks in these subjects were 60, 50 and 90 respectively. What is her percentage in the aggregate? _______
A fraction is undefined if it’s denominator is ____________
____________ is the process whereby the numerator of one side multiplies the denominator of the other side and vice versa and each product is equal to one another.
Bolu bought a stereo at 30% discount on its original price. He sold it with a 50% increase on the price he bought. What percentage of profit did he make on the original price? ____________
____________ is the least possible mistake to be obtained in a given result.
____________ is the area of modern Mathematics that considers algebraic structures to be sets with operations defined on them, and extends algebraic concepts usually associated with the real number system to other more general systems, such as groups, rings, fields, modulus and vector spaces.
The length of a rectangular field in 20m and its breadth is 10m, if the length is increased by 60% and its breadth is increased by 50%, it’s area will be increased by ____________
A three digit angle measured from north in a clockwise direction is called ____________
____________ is an equation used to describe a relationship between two or more variables.
The population of a town in the year 2004 was 75,000. If the rate of increase of the population is 20% per annum, what will be its population in 2008? ____________
____________ represents the depth of an object when working with 3D coordinates.
A shape is a called a polygonal pyramid when the base is ____________
The subset of the co-domain which is a collection of all the images of the elements of the domain is called the ____________
After spending 75% of her income and giving 5% of the remainder in charity. Bimbo is left with N460.75. What is her monthly income? ____________
The point where the tangent touches the line is called ____________
The process of differentiating implicit function is called ____________
0.45 of 0.4 of a number is 36. What is the number? ____________
The adjoint matrix of a matrix A denoted by Adj A is the transpose of the matrix formed by substituting each element of the matrix A by its ____________
What is the decimal 0.005 written out in words? ____________________________________
The set of elements or members relevant to a particular application is called the ____________
A law enforcement agency receives a report of a drunk driver on the roadways on August 16 at 11:42p.m and another at 2:19a.m on August 17. How much time has elapsed between reports? ____________
The ____________ of a set is the number of elements the set contains.
Irrational numbers obtained from the square roots of rational numbers are called ____________
A geometric progression is a sequence of numbers in which each term other than the first is obtained from the preceding one by the multiplication of a non-zero constant number called the ____________
A rectangular tank is 5 meters long and 0.6 metre wide. The water in it is 0.74m deep. If 1cu metre contains 1000 litres of water, find the amount of water in the tank. ____________
One of the most important practical application of arithmetic series is in the calculation of compound interest. YES/NO ____________
Is x3 + 1/x a polynomial? YES/NO ____________
Three cubes of sides 3, 4 and 5cm respectively are melted to form a new cube. Find the side of the new cube. ____________
A ____________ is a rectangular array of numbers enclosed within brackets.
____________ is the process of transferring one quantity from one side of an equation to the other side whereby the quantity involved changes its sign to the opposite sign.
During the week of cloth sales, all cloth was reduced in the same ratio. If a cloth costing N840 was offered at N640, what would be the sale price of a cloth costing N1050 originally? ____________
When a quadratic has the form ax2=c it is called ____________
When two triangles have two of their sides and an included angle corresponding equal, the congruence is called ____________
If the population of yeast cells grows from 30 to 1920 in a period of 6 hours, what is the rate of growth? ____________
____________ is the number which corresponds to a given logarithm.
____________ of an angle is trigonometric function of the ratio of the adjacent and hypotenuse sides of any angle in right angled triangle.
Write 5 million two hundred and six thousand eight in numerals. ____________________________________
____________ of a triangle is a line perpendicular to the base.
The formula for the last term T of a Geometric Progression is ____________
A salesman buys 600 mangoes daily and sells them at 80 kobo per dozen. How much money does he earn in half a year? ____________
____________ is a number expressed as an ordered pair comprising of real number and an imaginary number, written in the form a+bi, where a and b are real numbers, and i is the imaginary unit.
____________ property is whereby summing two numbers and then multiplying by another number yields the same value as multiplying both values by the other value and then adding them together.
A typist uses a sheet of paper of 20cm x 28cm for typing. He leaves a margin of 4cm on either side and 5cm on top and bottom. What fractional part of the paper is used for typing? ____________
The mathematical operation where a number (the base) is multiplied by itself a specified number of times (the exponent) is called ____________
____________ is a type of conic section curve, any point of which is equally distant from a fixed point and a fixed straight line.
5 men can complete a job in 4 days. What fraction of the job can a man do in one day? ____________
The ____________ of set A and B is the set which consists of elements that are either in A or B or both.
If the determinant of a square matrix is equal to zero, the matrix is called ____________
6¾ dozen biros cost N82, what will be the cost of 3⅜ dozens of these biros? ____________
Write the predecessor of 800000 ____________
Write the successor of 999999 ____________
If Y X and if in addition there is at least one element of X which is not in Y, then Y is a ____________ of X.
The difference between the amount and the original principal is called the ____________
When a rectangle is inserted in a circle and the four vertices touching the circle, it is called ____________
The ____________ of a figure is the side that is perpendicular to the height.
What number can replace the asterisk mark in the number 59*3 such that the number is divisible by 9? ________
____________ is the portion of a circle bounded by 2 radii.
____________ is the product of all consecutive integers up to a given number (used to give the number of permutations of a set of objects).
A married couple has eight sons and six daughters. The sons gave birth to four children each while the daughters gave birth to 5 children each. How many members are there in the family? ____________
____________ is a subsidiary collection of objects that all belong to, or is contained in, an original given set.
A shape which has no lines of symmetry is called ____________
In a University hall, there are 1,681 chairs arranged in such a way that row contains as many chairs as the number of chairs in a row. What is the number of chairs in each row? ____________
____________ is a method of solving probability questions by listing all the outcomes of an event and the probabilities are calculated by multiplying down the branches.
The distance between the apex and the meeting points of the diagonals of a base is called ____________
What is the product of the largest and smallest four digit numbers formed by using the digits 5, 6, 1 and 2? ____________
The set of all the subsets of a set is called ____________
____________ is about arrangement of things about a circular object.
There is a piece of cloth 680cm long and 160cm wide. Square handkerchiefs of maximum size are to be made from this cloth so that there is no wastage of the cloth. Find the length of each handkerchief? ____________
The arrangement of objects in which order is not taken into account is called ____________
The straight line, perpendicular to the tangent at the point of contact of the tangent to the curve is called the ____________ to the curve.
An even number when added to another prime number will result in prime and odd numbers only? YES/NO _____
The angle subtended at the centre of the great or small circle by the minor arc joining two places in the great or small circle is called ____________
The distance of the arc of a great circle subtending an angle of 1 minute at the centre of the Earth is called ________________________
Four bells begin tolling at the same time and continue to do so at intervals of 22, 26, 28 and 30 seconds respectively. The bells will toll together after every ____________ seconds.
Longitude 00 is called ____________
If the three angles of one triangle are respectively equal to the three angles of another, the two triangles are ____________
Every set is a subset of itself and also a subset of the ____________
Akin ranked 11th from the top and 40th from the bottom in a class. How many students are there in the class?
If two finite sets A and B are disjoint, then n(AᴜB)= ____________
Discuss the following with at least 100 words: Inscribed and E-scribed Circles, Longitude and Latitude, Cosine Rule and Sine Rule.
Joke is getting married 2 days later, at an outdoor ceremony in the desert. In recent years, it has rained only 10days each year. Unfortunately, the meteorologist has predicted rain for 2days time. When it actually rains, the meteorologist correctly forecasts rain 80 of the time. When it doesn’t rain, he incorrectly forecasts rain 20 of the time. What is the probability that it will rain on the day of Joke’s wedding? ____________
If the mean of the numbers u, w, x, y, z is a, find the mean of u+b, w+2b, x-b, y-2b, z.
The mode of the positive integers 4, 6, 9, 11, 12, 19, a, b is 9 and their mean is b. Find the values of a and b.
Calculate the centre and radius of the circle 4x2 + 4(y- 6/4)2=4
Make n the subject of the relation Sn = n/2[2a+(n-1)d]
A lady invested a total of N100,000 in two companies which paid dividends of 14% and 10% respectively. If she received a total of N13,200, calculate how much did she invest at both rates?
Find the values of y in (30x3-1) + 1 = 10
1 + 1 y
3-1 + 1/y
X and Y are points on the parallel of latitude 700N, their longitudes being 1370W and 430E respectively. Calculate the following:
The distance measured apart along the parallel of latitude
The distance measured apart along the great circle.
Let U be a square matrix of order n. Define a Matrix Ui by means of the formula: Ui = iU+(1-i)UT
Compute Ui explicitly for i = ½, 1 and 2 if U =
The expression ax2 + bx + c is a ____________ equation.
Peter Venn was the originator of Venn Diagrams. YES/NO ____________