Linear diagrams show sets as lines going across the diagram horizontally, and show set intersections by the vertical overlap of lines.
Generate your own linear diagram here: Linear Diagram Generator .
This diagram indicates that some things are both dogs and mammals, as there is an overlap between the two
lines. Also, dogs and mammals have sections which overlap with pets, so some things are all of dogs,
mammals and pets.
As there is no point where the line for dogs does not overlap with the line for mammals,
then all dogs are mammals. However, there is an section of the mammals line which does not
overlap with dogs, so some mammals are not dogs.
The following specifiation was used to create the diagram in the Linear Diagram Generator
pet
mammal
pet mammal
mammal dog
dog mammal pet
The above linear diagram gives the same information as this Euler diagram:
Linear Diagrams can also be used to show values associated with the set intersections. These are called "length proportional linear diagrams". For example:
The following specifiation was used in the linear diagram generator Note how all the intersections are followed by a numerical value:
English 15
History English 4
Geography English 7
This diagram shows some of the subjects that students in a school class are taking. The part of the line where History and English
overlap is quite short, as only 4 students are taking both of these subjects. This is the smallest length as it represents the smallest number of students. This also corresponds to the total number of students taking History as this is the only overlap that includes the subject.
The section where English overlaps with no other subject is the longest, as the most students, 15, are taking only this subject. All 26 students are taking English as there is no point where there is an overlap that does not include this subject.
There is no overlap between History and Geography as no students are taking both of those subjects.
The above linear diagram gives the same information as this area proportional Euler diagram, adapted from the Euler3 area proportal diagram generator:
So far, the diagrams have been simple, and the equivalent Euler diagrams have been readily interpretable. This is intentional, the first two examples were created to make both sorts of diagram easy to understand. However, as the specification of diagrams become more complex, we can demonstrate the effectiveness of linear diagrams. Euler diagrams can become very difficult to read, even at three sets. To see this, use the Random Diagram button of this Euler diagram generator.
Here we show a seven set linear diagram, which can be regenerated here, followed by its Euler diagram equivalent. Again, it shows academic subjects studied by students, but this time without any values associated with the overlaps. The example is taken from an investigation into the effectiveness of these diagrams, see the Set Study.
The concurrent lines make it difficult to see what subjects are represented by each region of the Euler diagram, but from the
linear diagram it is relatively easy to see that there are students studying all of Biology,
Geology and Design, but no one is studying all of Geology, Physics
and Chemistry.
Similarly, the complete overlap of of Music by Design means all who study Music also study Design. Also, the disjointness between between Geology, History and Music is evident from the linear diagram, by the lack of overlap of the three lines.
Contact: Peter Rodgers email: P.J.Rodgers@kent.ac.uk