# Circle charts middle meet

### Circle Geometry

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Slices that cover half or a quarter of the circle will therefore stand out. Others can be compared with some success, but reading actual numbers from a pie chart is next to impossible. As a consequence, numbers usually need to be shown as well, and the number of slices needs to be limited to allow the viewer to get an overview without having to try to read the chart in detail which is frustrating.

Which is larger in the following chart, the black or the yellow slice?

## Venn diagram

What about black and green? How sure are you? And where do you look to compare? Now compare this to the bar chart.

## Three circles

There is no doubt which is larger, or by how much. When you care about comparing the parts, a bar chart is clearly superior. What the bar chart does not convey, though, is the part-whole relationship: What the bar chart does not let you do easily is compare one bar to the sum of all bars: Pie Chart Mistakes Care must be taken to retain the salient feature of the chart: In a report on the number of words consumed each daya pie chart was prettified with a highlight in the middle.

That obscures the spot where the lines meet, and thus makes it impossible to judge angles, making the comparison more difficult. This is similar to the problem with a colleague of the pie chart, the donut chart.

It is similar to the pie chart, but is missing a circular area in the center. The comparison between separate pie or donut charts is also largely meaningless, and should be avoided. To show progression over time, line and bar charts are much better suited.

To compare two different kinds of data absolute numbers and fractionsit makes more sense to split them up by data to compare than by year. Other distortions include the ubiquitous 3D pie chart, which introduces perspective distortion and requires our very underdeveloped sense of depth to make up for it.

These charts may be more spectacular, but in terms of communicating data, they are mostly useless. Number of Slices The most common problem is trying to show too many categories in a single pie chart. Wikipedia has this beautiful specimen on the page on U. The first four states are clearly larger than any of the rest, and from there the chart turns from a meaningful visualization of numbers into a colorful pattern. A bar chart would have been a much better idea here, because it would have allowed easier comparison between the states.

### Tableau Tip: How to make KPI donut charts

Grouping together states of similar size into separate charts with different scales would have made it possible to clearly see the differences for all of them, not just the most populous ones. When to Use Pie Charts There are some simple criteria that you can use to determine whether a pie chart is the right choice for your data. Do the parts make up a meaningful whole?

If not, use a different chart. Only use a pie chart if you can define the entire set in a way that makes sense to the viewer. Are the parts mutually exclusive? If there is overlap between the parts, use a different chart. Do you want to compare the parts to each other or the parts to the whole?

If the main purpose is to compare between the parts, use a different chart. The main purpose of the pie chart is to show part-whole relationships. How many parts do you have? The diagram below shows that given a line and a circle, can arise three possibilities: The line may be a secant, cutting the circle at two points.

The line may be a tangent, touching the circle at just one point. The line may miss the circle entirely. The point where a tangent touches a circle is called a point of contact.

It is not immediately obvious how to draw a tangent at a particular point on a circle, or even whether there may be more than one tangent at that point. Theorem Let T be a point on a circle with centre O. Proof First we prove parts a and c. Let be the line through T perpendicular to the radius OT.

Let P be any other point onand join the interval OP. Hence P lies outside the circle, and not on it. This proves that the line is a tangent, because it meets the circle only at T. It also proves that every point onexcept for T, lies outside the circle.

It remains to prove part b, that there is no other tangent to the circle at T. Let t be a tangent at T, and suppose, by way of contradiction, that t were not perpendicular to OT.