Copyright protection on math problems

[jason_cncma]

I was wondering exactly what was protected on a copyrighted math problem. I know 1 + 1 = 2 is not copyrightable, but I believe that word problems are. If I wanted to use a copyrighted math problem as closely as possible w/o breaking the law, what would have to be changed from the math problem in order to be legal?

That is, if I change one word, or a number or a name, is that ok or is that not enough? Also, what if there are pictures involved? Can they be copyrighted too or is it just the text? Thanks for the help!

 

[The Occultist]

If I might ask: just what, precisely, are you trying to do?

Also, what state are you in? This site is for US law only.

 

[thedoctorisin]

If I wanted to use a copyrighted math problem as closely as possible w/o breaking the law, what would have to be changed from the math problem in order to be legal?

Making derivative works is protected by the copyright, so if you start off with the copyrighted problem as your base/model, it doesn't matter how much you change - you will still need the permission of the copyright holder.

 

[jason_cncma]

More food for thought

Occultist, I live in Mass and I am trying to make an SAT prep course that has questions that are as close to real SAT questions as possible without violating copyrights.

thedoctorisin, I understand what you mean when you say that I cannot change a problem when I'm making "derivative work". But there is a point where things are changed so much that it's no longer protected or traceable to the original problem for that matter. If what you say is true, no one could claim to make SAT-style questions without infringing copyright since there are a finite number of ideas for math questions out there. In other words, I could take any real SAT question and find a 3rd party SAT-review question that is close enough that one could argue it was a "derivative work".

I think this issue needs further investigation. Below are some real copyrighted SAT questions that are followed by my own personally modified versions that are derivative works from the copyrighted versions. I could understand that some of my questions could infringe on copyrights, but there is no way that they ALL do since I've added a reasonable amount of "artistic content" in many different ways. That is, if these questions appeared in competing text books, I don't think anyone could complain? I'm not saying I don't believe in what you say, thedoctorisin, especially since I'm the naive although educated person asking the legal questions. I'm just saying that it doesn't make sense to me and the following examples might show why. I beleive that I may have added my own "artistic content" to make these questions my own. Again I may be totally wrong, but I think given my layman knowledge base it makes pretty good sense. (Note that I've chosen several styles/lengths of questions to examine)

Example 1 (accompanied by a parabola graphed out on an XY-plane)
In the figure above, PQRS is a rectangle, and points Q and R lie on the graph of y = ax^2, where a is a constant. If the perimeter of PQRS is 10, what is the value of a?

I)(With same picture)
PQRS is a rectangle that intersects the graph y = ax^2 on points Q and R on the diagram above. If the distance around PQRS is 10, what is the value of the constant a in y = ax^2?

II)(no picture... enough data is actually in the problem to solve it w/o the picture)
Rectangle PQRS intersects the graph y = ax^2 (where a is a constant) on two points, P and Q. If the perimeter of PQRS is 10, what is the value of a?

III)When a is a constant, the graph y = ax^2 intersects rectangle PQRS on points P and Q. If the perimeter of PQRS is 10, find the value of a.


Example 2 (no picture, Just an obervation, but is this question even copyrightable? It doesn't seem to contain any creative elements as many questions of this nature appear in every algebra textbook on the planet)
If ab + b = a + 2c, what is the value of b when a = 2 and c = 3?

I)When ab + b = a + 2c, if a = 2 and c = 3, find the value of b.

II)Consider the equation ab + b = 2c. If a = 2 and c = 3, solve for b.

III)What is the value of b in the equation ab + b = 2c when a = 2 and c = 3?


Example 3 (a function appears above the actual question)
h(t) = c - (d -4t)^2
At time t = 0, a ball was thrown upward from an initial height of 6 feet. Until the ball hit the ground, its height, in feet, after t seconds was given by the function h above in which c and d are positive constants. If the ball reached its maximum height of 106 feet at time t = 2.5, what was the height, in feet, of the ball at time t = 1?

I)
(Assume function doesn't appear above)
A ball was thrown upward from a fixed location 6 feet off the ground. After the ball was thrown, it's height, in feet, can be represented by the function h(t) = c - (d- 4t)^2. t = time in seconds, h = height while c and d are both positive constants. If the maximum height of 106 feet was reached 2.5 seconds after the ball was thrown, what was the height, in feet, 1 second after the ball was thrown?

II)
h(t) = c - (d - 4t)^2
At time t = 0, a ball is at rest 6 feet off the ground on a platform. It is launched from a cannon in an upward trajectory where the height of the ball is represented in the function h(t) above where t is time in seconds while c and d are positive constants that represent gravity. If the ball reached its maxium height of 106 feet after 2.5 seconds, what was the height after 1 second?

III)
h(t) = c - (d - 4t)^2
The function above represents the height of a tennis ball hit off a raquet from a cliff 6 feet above the water level of the ocean. After 2.5 seconds, the ball is 106 feet in the air. If c and d are both positive constants while t represents time in seconds, what would be the height of the ball after 1 second?

Example 4 (a chart is above that is titled "OUTDOOR SNEAKER COMPANY'S JULY PRODUCTION" with 3 x 3 spreadsheet containing both empty/non-empty cells)
Outdoor Sneaker Company manufactures only white sneakers and black sneakers, both of which are available as high-tops or low-tops. On the basis of the information in the table above, how many black sneakers did Outdoor Sneaker Company manufacture in July?

I)
(chart appears with same exact data with different title)
Neverbreak condoms features standard or glow-in-the-dark condoms that are either smooth or ribbed. If you consider the chart above, how many ribbed condoms were produced last year?


Example 5 (3 points are given and are displayed above the question text itself)
P(3,2)
Q(7,2)
R(7,4)
The coordinates of points P, Q, and R in the xy-plane are given above. What is the perimeter of triangle PQR?

I)(instead of listing points, show a triangle picture with the points clearly labeled)
What is the perimeter of triangle PQR?

II)(show no points above the question text)
If the vertices of a triangle are (3,2), (7,2) and (7,4), what is the perimeter?

III)Find the perimeter of triangle PQR when P(3,2), Q(7,2) and R(7,4)

Anyways, at the end of the day I think that my point is that there is a line that I can come close to without crossing when it comes to copyrighting math questions. What I want is some sort of concrete description of what that line is so I can be sure to never cross it. Thanks again for everyone's help!

~Jason

 

[thedoctorisin]

But there is a point where things are changed so much that it's no longer protected

Sorry, you are wrong. there is no such point.

or traceable to the original problem for that matter.

In other words, you are asking how you can break copyright law and not get caught.

If what you say is true, no one could claim to make SAT-style questions without infringing copyright since there are a finite number of ideas for math questions out there. In other words, I could take any real SAT question and find a 3rd party SAT-review question that is close enough that one could argue it was a "derivative work".

You seem to think that the only relevant/admissible evidence in a copyright case is how close the second work is to the original. Should you choose to continue in your illegal endeavor, you will quickly find out otherwise, because the College Board people aren't shy about suing for copyright infringement. They put a ton of effort/money into creating those questions, and they don't like it when others try to steal that effort for their own profit.

People who create their own math problems from scratch invest a lot of hard work into that effort, and would therefore have a lengthy evidence trail that proves the independent creation of those problems, regardless of any random similarities that might show up.

I beleive that I may have added my own "artistic content" to make these questions my own.

No matter how much content you add, it is still a derivative work. Just FYI, the dead giveaway in your problems is that you have not changed the "mathematical content" one iota, except to delete pictures that really are relevant to the problem.

II)(no picture... enough data is actually in the problem to solve it w/o the picture)
Rectangle PQRS intersects the graph y = ax^2 (where a is a constant) on two points, P and Q. If the perimeter of PQRS is 10, what is the value of a?

You cannot determine the value of a from the above information. For example, a could be 1, with P(-1,1), Q(1,1), R(1,-2), S(-1,-2). Or a could be 2, with P(-1,2), Q(1,2), R(1,-1), S(-1,-1).

Anyways, at the end of the day I think that my point is that there is a line that I can come close to without crossing when it comes to copyrighting math questions.

There is no such line. If you create a derivative work from an SAT question without permission, and they can prove it in court, then you are in trouble, regardless of how much you have changed things. Your posts here are a "smoking gun" that clearly indicate your intent to violate copyright law. I doubt you could provide, under cross-examination, any mathematically relevant details about the sample questions that you posted. For example, what mathematical laws were you trying to test when you came up with question 2? Associative law? Commutative law? What is the significance of your choice of the -4 coefficient for t in question 3? How does it relate to the physical significance of the problem? Could it be changed to another value?

What I want is some sort of concrete description of what that line is so I can be sure to never cross it.

Then create your own math problems from scratch.

 

[divgradcurl]

Making derivative works is protected by the copyright, so if you start off with the copyrighted problem as your base/model, it doesn't matter how much you change - you will still need the permission of the copyright holder.

That's not the definition of a derivative work. If the OP only uses the non-copyrightable parts of the original to create his own work, there cannot be a derivative work, because the parts he used aren't protected under copyright anyway.

 

[divgradcurl]

Occultist, I live in Mass and I am trying to make an SAT prep course that has questions that are as close to real SAT questions as possible without violating copyrights.

thedoctorisin, I understand what you mean when you say that I cannot change a problem when I'm making "derivative work". But there is a point where things are changed so much that it's no longer protected or traceable to the original problem for that matter. If what you say is true, no one could claim to make SAT-style questions without infringing copyright since there are a finite number of ideas for math questions out there. In other words, I could take any real SAT question and find a 3rd party SAT-review question that is close enough that one could argue it was a "derivative work".

I think this issue needs further investigation. Below are some real copyrighted SAT questions that are followed by my own personally modified versions that are derivative works from the copyrighted versions. I could understand that some of my questions could infringe on copyrights, but there is no way that they ALL do since I've added a reasonable amount of "artistic content" in many different ways. That is, if these questions appeared in competing text books, I don't think anyone could complain? I'm not saying I don't believe in what you say, thedoctorisin, especially since I'm the naive although educated person asking the legal questions. I'm just saying that it doesn't make sense to me and the following examples might show why. I beleive that I may have added my own "artistic content" to make these questions my own. Again I may be totally wrong, but I think given my layman knowledge base it makes pretty good sense. (Note that I've chosen several styles/lengths of questions to examine)

Example 1 (accompanied by a parabola graphed out on an XY-plane)
In the figure above, PQRS is a rectangle, and points Q and R lie on the graph of y = ax^2, where a is a constant. If the perimeter of PQRS is 10, what is the value of a?

I)(With same picture)
PQRS is a rectangle that intersects the graph y = ax^2 on points Q and R on the diagram above. If the distance around PQRS is 10, what is the value of the constant a in y = ax^2?

II)(no picture... enough data is actually in the problem to solve it w/o the picture)
Rectangle PQRS intersects the graph y = ax^2 (where a is a constant) on two points, P and Q. If the perimeter of PQRS is 10, what is the value of a?

III)When a is a constant, the graph y = ax^2 intersects rectangle PQRS on points P and Q. If the perimeter of PQRS is 10, find the value of a.


Example 2 (no picture, Just an obervation, but is this question even copyrightable? It doesn't seem to contain any creative elements as many questions of this nature appear in every algebra textbook on the planet)
If ab + b = a + 2c, what is the value of b when a = 2 and c = 3?

I)When ab + b = a + 2c, if a = 2 and c = 3, find the value of b.

II)Consider the equation ab + b = 2c. If a = 2 and c = 3, solve for b.

III)What is the value of b in the equation ab + b = 2c when a = 2 and c = 3?


Example 3 (a function appears above the actual question)
h(t) = c - (d -4t)^2
At time t = 0, a ball was thrown upward from an initial height of 6 feet. Until the ball hit the ground, its height, in feet, after t seconds was given by the function h above in which c and d are positive constants. If the ball reached its maximum height of 106 feet at time t = 2.5, what was the height, in feet, of the ball at time t = 1?

I)
(Assume function doesn't appear above)
A ball was thrown upward from a fixed location 6 feet off the ground. After the ball was thrown, it's height, in feet, can be represented by the function h(t) = c - (d- 4t)^2. t = time in seconds, h = height while c and d are both positive constants. If the maximum height of 106 feet was reached 2.5 seconds after the ball was thrown, what was the height, in feet, 1 second after the ball was thrown?

II)
h(t) = c - (d - 4t)^2
At time t = 0, a ball is at rest 6 feet off the ground on a platform. It is launched from a cannon in an upward trajectory where the height of the ball is represented in the function h(t) above where t is time in seconds while c and d are positive constants that represent gravity. If the ball reached its maxium height of 106 feet after 2.5 seconds, what was the height after 1 second?

III)
h(t) = c - (d - 4t)^2
The function above represents the height of a tennis ball hit off a raquet from a cliff 6 feet above the water level of the ocean. After 2.5 seconds, the ball is 106 feet in the air. If c and d are both positive constants while t represents time in seconds, what would be the height of the ball after 1 second?

Example 4 (a chart is above that is titled "OUTDOOR SNEAKER COMPANY'S JULY PRODUCTION" with 3 x 3 spreadsheet containing both empty/non-empty cells)
Outdoor Sneaker Company manufactures only white sneakers and black sneakers, both of which are available as high-tops or low-tops. On the basis of the information in the table above, how many black sneakers did Outdoor Sneaker Company manufacture in July?

I)
(chart appears with same exact data with different title)
Neverbreak condoms features standard or glow-in-the-dark condoms that are either smooth or ribbed. If you consider the chart above, how many ribbed condoms were produced last year?


Example 5 (3 points are given and are displayed above the question text itself)
P(3,2)
Q(7,2)
R(7,4)
The coordinates of points P, Q, and R in the xy-plane are given above. What is the perimeter of triangle PQR?

I)(instead of listing points, show a triangle picture with the points clearly labeled)
What is the perimeter of triangle PQR?

II)(show no points above the question text)
If the vertices of a triangle are (3,2), (7,2) and (7,4), what is the perimeter?

III)Find the perimeter of triangle PQR when P(3,2), Q(7,2) and R(7,4)

Anyways, at the end of the day I think that my point is that there is a line that I can come close to without crossing when it comes to copyrighting math questions. What I want is some sort of concrete description of what that line is so I can be sure to never cross it. Thanks again for everyone's help!

~Jason

Cleary the mathematical equations are not copyrightable, nor are the correct results. The incorrect results may be copyrightable, though.

Your best bet is to create your own set of math problems that are of the same type and content, and create your own practice tests. It's more work, but should avoid crossing any lines.

But you certainly can look to other SAT prep books to find the types of questions you want to create -- simply looking at something else, or gaining inspiration from something else, does not create a derivative work.