Difference Between a Percentage and a Rate (as explained by medical field) Often we hear the question, "What is the difference between a percentage and a rate?" They are both calculated using a numerator and a denominator. However, the relationship between the numerator and denominator makes the difference. Percentages Indicators which use percentage are the most commonly used indicator type in healthcare. Guidelines for Percentages: Numerator and denominator are the same unit of measure Both the numerator and denominator are positive whole numbers The numerator is never greater than the denominator Example: An AMI patient is admitted. Percentages are charted on a p chart, where p stands for proportion. Rates A rate, on the other hand, does not have the same numerator-denominator relationship as a percentage. If we answer the question, "Can an outcome happen more than once in an area of opportunity?" Guidelines for rates: Example: We might measure the number of falls per 1000 patient days. Let me give you one more example that may help to illustrate the difference.
Welcome to the Institute for Mathematics and its Applications (IMA) Similar Triangles Applications Image Source: A powerful Zoom lens for a 35mm camera can be very expensive, because it actually contains a number of highly precise glass lenses, which need to be moved by a tiny motor into very exact positions as the camera auto focuses. The Geometry and Mathematics of these lenses is very involved, and they cannot be simply mass produced and tested by computer robots. Lots of effort required to manufacture these lenses results in their very high price tags. Here is a diagram showing how the zoom lens internal arrangement changes as we zoom from 18mmm wide angle to 200mm fully zoomed in: Image Source: Image Copyright 2013 by Passy’s World of Mathematics Shown above are some band photographs taken by Passy with a special low light camera. Unfortunately this camera does not have a zoom lens, and so you need to be right up close to the stage to take good pictures. Measuring heights of tall objects is also covered in this lesson. Bow Tie Triangles
La Gaceta de la RSME Noticias de la Sociedad Inauguración del año del Centenario de la Real Sociedad Matemática Española: Desarrollo del acto de Apertura del Centenario Redacción de La Gaceta Intervención de la Presidenta del Comité para la Celebración del Centenario María Jesús Carro Rossell Intervención del Presidente de la RSME Antonio Campillo López Intervención del Ministro de Educación Ángel Gabilondo Pujol Memoria de actividades de la Real Sociedad Matemática Española: 1997-2010 Henar Herrero, Ramón Esteban, Pablo Fernández, Patricio Cifuentes y Salvador Segura Actualidad Tesis de Matemáticas defendidas en España en el año 2010 Redacción de La Gaceta Conclusiones del Seminario CEMat 2010 Comisión de Educación del CEMat Reseña de libros y revistas «Linear Functional Analysis», de Joan Cerdà José Luis González Llavona «An Introductory Course on Mathematical Game Theory», de Julio González Díaz, Ignacio García Jurado y M. Artículos Problemas y Soluciones Problemas propuestos: números 169 al 174 Educación Historia
Aspect Ratios in Photography This article is written by Andrew S. Gibson, the author of Square. Today I’d like to draw your attention to an area of composition that you might not have given much thought to: aspect ratio. Aspect ratio is the term used to describe the dimensions of an image by comparing the width to the height and expressing it in ratio form. The aspect ratio of your images is primarily determined by the dimensions of your camera’s sensor (or the film type plus camera design with film cameras). As these physical aspects are fixed, it is easy to take the aspect ratio of your images for granted, and to not consider the implications of the aspect ratio you are using in relation to composition. Camera makers have realised that sometimes photographers like to work in different aspect ratios, and most recent digital cameras let you change the aspect ratio using the camera’s menu. Why aspect ratio matters Why does aspect ratio matter? What is aspect ratio? A full-frame 35mm sensor measures 36 x 24mm. Square
Some Mathematical GIFs Here are some GIFs I have collected over internet that explain mathematical ideas. The following GIF explain what is meant by tangent/parallel lines and asymptotes. The following GIF explains how to construct a regular heptagon using straight edge and compass. The following 2 GIFs explain what an ellipse is and how to draw it. The area of the circle with unit radius is and so is the circumference of the circle with unit diameter. The following GIF explain a method to find the Golden Ratio ( The following 3 GIFs are the illustrations of Pythagorean Theorem. If you move along a unit circle with center at origin, then its coordinates are . The following GIF explains that how a sine wave is compressed or expanded if its period is changed. The following GIF explain how to plot a graph by moving from rectangular to polar coordinates. The following 2 GIFs demonstrate the creation of cardoid. The following two GIFs demonstrate the creation of hypotrochoids. The last 3 GIFs are misc curves. Like this:
Stats: Binomial Probabilities Binomial Experiment A binomial experiment is an experiment which satisfies these four conditions A fixed number of trials Each trial is independent of the others There are only two outcomes The probability of each outcome remains constant from trial to trial. These can be summarized as: An experiment with a fixed number of independent trials, each of which can only have two possible outcomes. The fact that each trial is independent actually means that the probabilities remain constant. Examples of binomial experiments Tossing a coin 20 times to see how many tails occur. Examples which aren't binomial experiments Rolling a die until a 6 appears (not a fixed number of trials) Asking 20 people how old they are (not two outcomes) Drawing 5 cards from a deck for a poker hand (done without replacement, so not independent) Binomial Probability Function Example: What is the probability of rolling exactly two sixes in 6 rolls of a die? There are five things you need to do to work a binomial story problem.
The Unexpected Math behind Van Gogh's "Starry Night" A few lesson plans exist for teaching visual arts and self-similarity (objects that have the same pattern) that could be used after showing this lesson. Shodor has some free lesson plans for students in grades 4 through 8. High school students can learn recursion algorithms to create the Koch curve using Scratch for free. Educational technologist Dylan Ryder has also written about creating fractals. A beautiful app worth checking out is Starry Night Interactive App by media artist Petros Vrellis. Download it to your tablet and create your own version of Starry Night. Really interested in mathematics? Turbulence, unlike painting, is mostly a time-dependent phenomenon, and after some time, breaks statistical self-similarity that Kolmogorov predicted in the 1960s. In fluid mechanics, since we can't often solve the equation for flow patterns, we develop a system of scaling between the physical properties. AcknowledgementsNatalya St.
The Math Circle Fields Institute - Math Circles NEWS 2014: Math Circles Instructors wanted! (Apply here) Math Circles at the Fields Institute is looking for new volunteers to teach bright high school students interesting topics in mathematics. The goal of Math Circles is to introduce different topics in mathematics not necessarily taught in school, while keeping things fun! In particular, we are looking for instructors to do one of the following topics: Introduction to Real Analysis Introduction to Graph Theory Introduction to Topology Introduction to Groups and Rings The Game of Go Game Theory Optimization Other topics are welcome! Hello Advanced Math Circles, Sacha Mangerel will be teaching a series in Real Analysis over the next three weeks for the Advanced Group. - Construction of real numbers - Introduction to Cardinal arithmetic - Sequences and continuous functions - Derivatives and the Mean Value Theorem - Theory of Riemann integration an Fundamental Theorem of Calculus See you soon! LECTURE notes: Back to top
CEMC - Math Circles The Waterloo Math Circles is a free weekly enrichment activity for grade 6 to 12 students organized by the Faculty of Mathematics of the University of Waterloo. Registration All students interested in attending the Fall Math Circles in 2014/15 will need to register. Space in the program is limited – register early. Math Circles Materials Math Circles material, including presentation outlines and homework assignments, will be posted weekly. Intended Audience The meetings are accessible to interested students from grades 6 to 12. Dates and Location Math Circles will meet every Tuesday or Wednesday evenings, 6:30 to 8:30 p.m., from October 7/8 to November 25/26, 2014 and again from February 3/4 to March 31/April 1, 2015. All Math Circle meetings take place at the University of Waterloo (main campus). Room assignments for Fall session: Grade 6 Room: Tuesday and Wednesday, DC 1304 Grade 7/8 Room: Tuesday and Wednesday, DC 1302 Grade 9/10 Room: Wednesday, MC 1085; (except - Nov. 5 in MC 2034)
Math as Artistry I have a treat for readers today, an interview I did recently with Steven Strogatz, mathematician and writer on math extraordinaire. Strogatz is the Schurman Professor of applied mathematics at Cornell University. He is the author, most recently, of The Joy of x, a lovely book on math that grew out of his series of postings in the New York Times called the Elements of Math. How do I know Steve? GRANT: So, Steve, talk to me about the interesting part of math, the creative side. STEVE: Well, there’s a question part and an answer part to what we do. How do I know what to investigate or think about? Math is not just what we heard about in high school, the known and straightforward part of the subject. For me, I try to think about mathematizing parts of sciences that haven’t been understood mathematically, e.g. of social networks. GRANT: What then separates good from so-so mathematicians? STEVE: The quality of their creativity and the quality of their technique. Like this: Like Loading...
Dave's Short Trig Course Table of Contents Who should take this course? Trigonometry for you Your background How to learn trigonometry Applications of trigonometry Astronomy and geography Engineering and physics Mathematics and its applications What is trigonometry? Trigonometry as computational geometry Angle measurement and tables Background on geometry The Pythagorean theorem An explanation of the Pythagorean theorem Similar triangles Angle measurement The concept of angle Radians and arc length Exercises, hints, and answers About digits of accuracy Chords What is a chord? Ptolemy’s sum and difference formulas Ptolemy’s theorem The sum formula for sines The other sum and difference formulas Summary of trigonometric formulas Formulas for arcs and sectors of circles Formulas for right triangles Formulas for oblique triangles Formulas for areas of triangles Summary of trigonometric identities More important identities Less important identities Truly obscure identities About the Java applet.
Algebra - 1-(1x2)+1-(2x3)+1-(3x4)...+1-(n(n+1)) Hi Hossun. We need to give this a name so let f(n) = 1/(1x2)+1/(2x3)+1/(3x4)...+1/(n(n+1)). The first thing we notice is that for n > 1, we are just adding another fraction to the previous value of f(n). So we can construct f(n) = f(n-1) + 1/(n(n+1)). Now look at the small values of n: f(1) = 1/2, f(2) = 1/2 + 1/6 = 2/3, f(3) = 2/3 + 1/12 = 3/4, f(4) = 3/4 + 1/20 = 4/5, etc. So for the first few small values of n, we have proven by demonstration that f(n) = n / (n+1). Our task is to prove that if it works for any positive integer value of n, then it works for n + 1. Formally said, we need to prove that if for some positive integer n we can show that f(n) = n / (n+1), then we can conclude that f(n+1) = (n + 1) / (n + 2). We begin the real "proof" by expanding f(n + 1): f(n + 1) = f(n) + 1 / ((n+1)((n+1)+1)) because that's based on the construction. = n / (n+1) + 1 / ((n+1)(n+2)) because f(n) = n / (n+1); this is called "using what you know from earlier". Q.E.D. Cheers, Stephen La Rocque.