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What Is Visual Overlap In Math

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What Is A Venn Diagram

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A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits.

Venn diagrams help to visually represent the similarities and differences between two concepts. They have long been recognized for their usefulness as educational tools. Since the mid-20th century, Venn diagrams have been used as part of the introductory logic curriculum and in elementary-level educational plans around the world.

What Is And Isn’t An Adjacent Angle

Listed below are a few important points about what can be considered as an adjacent angle and what cannot be considered as adjacent angles even though it shares the same vertex and the side.

  • Adjacent angles share a vertex and a side as shown in the image below
  • Angles are not considered adjacent when they only share a vertex not a side
  • Angles are not considered adjacent angles when they only share a side, not a vertex
  • Angles are not considered adjacent when angles a and b overlap as shown in the image below

Applications For Venn Diagrams

Venn diagrams are used to depict how items relate to each other against an overall backdrop, universe, data set, or environment. A Venn diagram could be used, for example, to compare two companies within the same industry by illustrating the products both companies offer and the products that are exclusive to each company .

Venn diagrams are, at a basic level, simple pictorial representations of the relationship that exists between two sets of things. However, they can be much more complex. Still, the streamlined purpose of the Venn diagram to illustrate concepts and groups has led to their popularized use in many fields, including statistics, linguistics, logic, education, computer science, and business.

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How Do You Read A Venn Diagram

A Venn diagram is read by observing all of the circles that make up the entire diagram. Each circle is its own item or data set. The portions of the circles that overlap indicate the areas that are in common amongst the different items whereas the parts that do not overlap indicate unique traits among the item or data set represented by the circle.

Venn Diagram Purpose And Benefits

Figure 3 from Radial Sets: Interactive Visual Analysis of ...
  • To visually organize information to see the relationship between sets of items, such as commonalities and differences. Students and professionals can use them to think through the logic behind a concept and to depict the relationships for visual communication. This purpose can range from elementary to highly advanced.
  • To compare two or more choices and clearly see what they have in common versus what might distinguish them. This might be done for selecting an important product or service to buy.
  • To solve complex mathematical problems. Assuming youâre a mathematician, of course.
  • To compare data sets, find correlations and predict probabilities of certain occurrences.
  • To reason through the logic behind statements or equations, such as the Boolean logic behind a word search involving âorâ and âandâ statements and how theyâre grouped.

Diagramming is quick and easy with Lucidchart. Start a free trial today to start creating and collaborating.

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Why Visual Angles Are Important For Eye Tracking

Visual angles are everywhere in eye tracking. Researchers may want to ensure that their screen fits within the trackable range of their system where the trackable range is 32 degrees horizontally and 25 degrees vertically for example. Other researchers may want to ensure that stimuli on screen subtend exactly 5 degrees of visual angle, or that saccade targets appear at +/- 10 degrees of visual angle from the screen center. While the gaze data from eye trackers is generally reported in screen pixel co-ordinates, important metrics such as saccade amplitude and velocity are reported in degrees of visual angle / degrees per second. Also, gaze data is often parsed into saccades and fixations based on the eyes velocity which is measured by eye trackers in degrees per second. Finally, many critical measures of eye tracking data quality such as accuracy and precision are reported in degrees of visual angle. For example the EyeLink 1000 Plus is accurate to < 0.5 degs of visual angle.

Clearly, a basic understanding of the concept of visual angle can be very helpful in eye tracking research! The basic idea is illustrated below . The visual angle subtended by the flower is indicated by the purple double headed arrow.

Examples Of Overlap In A Sentence

overlapoverlapsoverlapVultureoverlap WSJoverlap NBC Newsoverlap The ConversationoverlapForbesoverlap IndyStaroverlapQuartzoverlapThe Arizona Republic

These example sentences are selected automatically from various online news sources to reflect current usage of the word ‘overlap.’ Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

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Converting Pixels To Degrees Of Visual Angle

Now that we can compute visual angle for objects that can be measured in mm, it is a relatively simple step to move between mm and screen pixels. If we know our screen pixel resolution as well as its dimensions it is very easy to work out how many pixels there are per mm. For example, in the horizontal direction, a screen with 1920 pixels, that measures 520mm wide, has 1920/520 = 3.89 pixels per mm. Another way of looking at things is to say that each pixel on the screen is 520/1920 = 0.27mm wide.

This conversion factor allows us to easily switch between pixels and mm, so we can also compute degrees of visual angle based on screen pixels. For example, a target presented 300 pixels to the right of the center of the screen described above is at = atan/700) = 6.6 degrees from the center.

An Online Visual Angle Calculator

Overlapping Triangle Problems

Whilst the math for calculating degrees of visual angle isnt too tricky , it is much easier to let a computer do it all for you which is why my colleague Jono from the support team created this handy online visual angle calculator just enter your screen resolution, dimensions, and distance, and it will convert between pixels and degrees of visual angle for you! Check it out you can find it and a couple of other handy apps in the Useful Apps tab on our learning resources page.

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The Definition And The Uses Of Venn Diagram

Venn Diagram For Math Youve probably seen or read about an Venn diagram prior to. Anyone who has attended Mathematics in particular Algebra and Probability, must already be familiar with this image. This is an image aid that is used to show the relationship between a set of items. Learn more about this commonly employed diagram in different fields and fields below.

Examples Of Venn Diagrams

A Venn diagram could be drawn to illustrate fruits that come in red or orange colors. Below, we can see that there are orange fruits such as persimmons and tangerines while apples and cherries come in red colors. Peppers and tomatoes come in both red and orange colors, as represented by the overlapping area of the two circles.

You might also draw a Venn diagram to help decide which of two cars to purchase. The Venn diagram shows the features that are exclusive to each car and the features that both cars have.

Below, we see that Car A is a sedan that’s powered by gasoline and gets 20 miles per gallon, while Car B is a hybrid, gets 40 miles-per-gallon for mileage, and is a hatchback.

The shaded region where the two circles overlap shows the features that both cars have in common, which include a radio, four doors, Bluetooth capability, and airbags.

The Venn diagram graphically conveys the similarities and differences between the two cars to help decide which to purchase.

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Understanding The Venn Diagram

The English logician John Venn popularized the diagram in the 1880s. He called them Eulerian circles after the Swiss mathematician Leonard Euler, who created similar diagrams in the 1700s.

The term Venn diagram did not appear until 1918 when Clarence Lewis, an American academic philosopher and the eventual founder of conceptual pragmatism, referred to the circular depiction as the Venn diagram in his book “A Survey of Symbolic Logic.”

Venn diagrams have been used since the mid-20th century in classrooms from the elementary school level to introductory logic.

Venn studied and taught logic and probability theory at Cambridge University, where he developed his method of using diagrams to illustrate the branch of mathematics known as set theory.

Venn published a precedent-setting work, “The Logic of Chance,” which explained the frequency theory of probability. In it, he argued that probability, contrary to popular assumption, should be established based on the regularity with which something is predicted to occur.

In another book, Symbolic Logic, Vennbuilt on and developed mathematician George Booles theories on algebra. This work helped him develop the Venn diagram.

How Much Do Two Rectangles Overlap


I have two rectangles a and b with their sides parallel to the axes of the coordinate system. I have their co-ordinates as x1,y1,x2,y2.

I’m trying to determine, not only do they overlap, but HOW MUCH do they overlap? I’m trying to figure out if they’re really the same rectangle give or take a bit of wiggle room. So is their area 95% the same?

Any help in calculating the % of overlap?

  • you mean to say, 2 rectangles are in a box with given co-ordinates?Feb 17 ’12 at 7:20
  • Did you give a try on that? If you have, what did you do?Feb 17 ’12 at 7:26
  • 1

Compute the area of the intersection, which is a rectangle too:

SI = Max - Max) * Max - Max)

From there you compute the area of the union:

SU = SA + SB - SI

And you can consider the ratio


While the accepted answer given is correct, I think it’s worth exploring this answer in a way that will make the rationale for the answer completely obvious. This is too common an algorithm to have an incomplete answer. Furthermore, with only a passing glance at the given formula, you may miss the beauty and extensibility of the algorithm, and the implicit decisions that are being made.

First, consider one way to define a two dimensional box is with:

  • for the top left point
  • for the bottom right point

This might look like:

I indicate the top left with a triangle and the bottom right with a circle. This is to avoid opaque syntax like x1, x2 for this example.

Two overlapping rectangles might look like this:

To summarize:

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What Is The Purpose And Benefits Of The Venn Diagram

The Venn diagram is used frequently across the globe of academia. Teachers at the school use the tool to teach mathematical concepts, such as intersections, sets, and unions. At higher mathematical levels its also used to tackle complicated problems. It is also possible to find diagrams within the field of statistics, particularly predictive analytics.

Beyond mathematics-related fields, it is also used to examine the similarities and distinctions between different languages. In the business world it is utilized to present comparisons of products as well as services. It is also used to display any other information relevant.

Heres the outline of the diagrams capabilities: could do:

  • Visually organize information to find connections between item sets.
  • No matter the level of complexity show the logic behind specific concepts, and use visual representation to demonstrate the connection between them.
  • When you are deciding on which products or services you want to purchase, compare several options and clearly see the similarities and distinctions between them.
  • Solve many mathematical problems.
  • Analyze the data set, discover correlations, and assess the probability of certain events.
  • Reason logic which supports equations or statements and how to group.

What Is The Icon That Looks Like An Eye

The eyeball icon simply means someone somewhere is watching your every move at that moment. On my phone it’s actually under settings> display> eye comfort. If its turned on the icon appears. The setting is to filter blue light which can become uncomfortable to eyes if looked into for a period of time./span>

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Simplest Way To Calculate The Intersect Area Of Two Rectangles

I have a problem where I have TWO NON-rotated rectangles and I like to calculate their intersect area. I have seen more general answers to this question, e.g. more rectangles or even rotated ones, and I was wondering whether there is a much simpler solution as I only have two non-rotated rectangles.

What I imagine should be achievable is an algorithm that only uses addition, subtraction and multiplication, possibly abs as well. What certainly should not be used are min/max, equal, greater/smaller and so on, which would make the question obsolete.

Thank you!

EDIT 2: okay, it’s become too easy using min/max or abs. Can somebody show or disprove the case only using add/sub/mul?

EDIT: let’s relax it a little bit, only conditional expressions are prohibited!

PS: I have been thinking about it for a half hour, without success, maybe I am now too old for this 🙂

Overlapping Bar Progress Graph

Overlapping Shape Drawing

One of the common messages reported in financial or operational reports is progress towards a goal. It could be a spending goal, production goal, or any other important metric that is tracked. The decision makers want to see the goal, where we expected to be at this time, and actual progress. Instead of the typical table of numbers, why not consider an overlapping bar progress graph line this.

This graph indicates the goal, planned progress, and actual progress visually, as well as indicating how far behind or ahead of plan we are at this time. The comparison to plan can be shown in percentage or in actual values like this example shows.

Because this visual is so compact, it can be used to show progress on a number of related metrics on a single slide or used in a dashboard visual.

This visual can be created in Excel using a standard bar graph where all the elements are driven by the data table so it can automatically update when the data changes. The rest of this article explains the steps to create this visual.

General approach

This visual is created by using a bar graph with five data series that overlap each other. The bars will represent the goal, the actual progress, the planned progress, the amount below plan, and the amount above plan. The below and above bars will display only when that situation is indicated. The bars are arranged in certain layer order so that only certain portions of underlying bars appear.

Data & Graph table setup

Adding data labels

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What Is The Definition Of Adjacent

Adjacent means when two things are side-by-side or next to each other. In a class, every bench has 2 students sitting next to each other is considered as adjacent. When states share a common boundary, we can refer them to as adjacent states as they are sharing the boundary and are next to each other. In math, adjacent is used to denote two sides or angles that lie next to each other, and we call them adjacent sides and adjacent angles.

The Venn Diagram: How Overlapping Figures Can Illustrate Relationships

There are lots of ways we can represent data in visual ways: a bar graph, a pie chart, an interpretive dance if you’re into that sort of thing. But one fun way to present information is through a Venn diagram, which tells you the ways in which things are different and similar by placing them in overlapping circles.

The use of Venn diagrams was first formalized by English philosopher and mathematician John Venn, who wrote a paper in 1880 entitled “On the Diagrammatic and Mechanical Representation of Propositions and Reasonings.” In this paper he suggested that formal logic could be presented in diagram form using what he called “Eulerian circles,” which are actually a bit different from what we now call Venn diagrams. While it’s certain Venn wasn’t the first to use overlapping circles to represent the relationships between data sets and he didn’t purport to have invented them people began to refer to them as “Venn diagrams.”

A Venn diagram is possibly the easiest type of diagram to understand you can look at it and immediately see what’s going on. Let’s just say you want to make a Venn diagram looking at the relationship between tomatoes and apples. First, you’d just make lists of descriptive terms about each: a tomato is red, mushy inside, red in the middle, round, savory tasting, smooth-skinned and a fruit. As for an apple, it is red, firm inside, white in the middle, round, sweet tasting, smooth-skinned and a fruit.

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Suggested Learning Targets #target

  • I can calculate the mean, range, and the mean absolute deviation to compare two data sets
  • I can observe the overlap and differences of two data sets with similar variability.
  • I can compare two data sets using the range or MAD.

The following diagrams show how to calculate the Mean Absolute Deviation. Scroll down thepage for examples and solutions on how to use the Mean Absolute Deviation.

Variability and Deviations from the MeanSummarizing Deviations from the Mean.

  • Variability describes how spread out the data is.
  • For any given value in a data set, the deviation from the mean is the value minus the mean.
  • The greater the variability of the distribution, the greater the deviations from the mean .

A consumers’ organization is planning a study of the various brands of batteries that are available.As part of its planning, it measures lifetime for each of six batteries of Brand A and eight batteries of Brand B. Dot plots showing the batterylives for each brand are shown below. Does one brand of battery tend to last longer or are they roughly the same? Justify your claim. What number could you calculate to compare the typical battery life of the two brands?

Introduction to Mean Absolute DeviationThis video explains what Mean Absolute Deviation is as well as how to calculate it.

Example:Find the Mean Absolute Deviation of the data2, 5, 7, 13, 18

Example:Find the Mean Absolute Deviation of the following data87, 94, 72, 65, 97, 77

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