Hey guys...
I had a crazy idea this morning at the gym. It probably came about from this reddit post I found a few weeks ago, and the related Stigler Diet.
Both of the above are attempts to formulate a mathematical optimisation model to find the optimal diet, perhaps minimised for cost. The constraints of the system would be that each nutrient must be present in the diet to some minimum value; and, in some cases, must be less than a maximum value.
So, I was thinking:
Suppose you represent every muscle in a vector, and every exercise in a vector. There is a matrix that relates each exercise to a set of muscles - each element in the matrix basically says "on a scale of 1 to something, how much is this muscle involved in this exercise?".
Parameters for each exercise include difficulty level (say, 1 to 10), exercise and rest time required, etc. User specified parameters would include weaknesses (the muscles that should be targeted more in the programme), injuries (the muscles that should be avoided where possible), etc. The user would elect the number of workout sessions in a period, and the time difference between each session. For example, a period may be a week and the sessions might be Monday, Wednesday, Friday - so the interval between the sessions would be about 2 days, 2 days, and 3 days respectively. The constraints of the system would ensure that a minimum amount of rest is given between each muscle group. The user would also elect the duration of each session, and, based on the time requirements of the exercise, the solution would include a workout that fits into the session interval.
There may also be another matrix which relates each exercise to each joint in each direction, and the flexibility requirement. For example, front squats with the clean grip require a minimum flexibility in the elbows.
The model can be as detailed or simple as desired. As long as the model accurately represents the real life scenario, the solution should make sense and would be tailored to the person's specific strengths, weaknesses, and goals.
A quick search of Google Scholar would seem to suggest that this application hasn't been investigated before. I'm an applied mathematician so I'm always looking for new and interesting things that can be modelled and solved (Such as the seating plan at our wedding that was solved my a simple quadratic programming model). All this is in my area of research - large scale combinatorial optimisation.
Since I don't have a huge amount of time around work/study/gym; I was thinking of setting up a project - perhaps on GitHub - and making it a community project released under GPL. What do you guys think?
I had a crazy idea this morning at the gym. It probably came about from this reddit post I found a few weeks ago, and the related Stigler Diet.
Both of the above are attempts to formulate a mathematical optimisation model to find the optimal diet, perhaps minimised for cost. The constraints of the system would be that each nutrient must be present in the diet to some minimum value; and, in some cases, must be less than a maximum value.
So, I was thinking:
Suppose you represent every muscle in a vector, and every exercise in a vector. There is a matrix that relates each exercise to a set of muscles - each element in the matrix basically says "on a scale of 1 to something, how much is this muscle involved in this exercise?".
Parameters for each exercise include difficulty level (say, 1 to 10), exercise and rest time required, etc. User specified parameters would include weaknesses (the muscles that should be targeted more in the programme), injuries (the muscles that should be avoided where possible), etc. The user would elect the number of workout sessions in a period, and the time difference between each session. For example, a period may be a week and the sessions might be Monday, Wednesday, Friday - so the interval between the sessions would be about 2 days, 2 days, and 3 days respectively. The constraints of the system would ensure that a minimum amount of rest is given between each muscle group. The user would also elect the duration of each session, and, based on the time requirements of the exercise, the solution would include a workout that fits into the session interval.
There may also be another matrix which relates each exercise to each joint in each direction, and the flexibility requirement. For example, front squats with the clean grip require a minimum flexibility in the elbows.
The model can be as detailed or simple as desired. As long as the model accurately represents the real life scenario, the solution should make sense and would be tailored to the person's specific strengths, weaknesses, and goals.
A quick search of Google Scholar would seem to suggest that this application hasn't been investigated before. I'm an applied mathematician so I'm always looking for new and interesting things that can be modelled and solved (Such as the seating plan at our wedding that was solved my a simple quadratic programming model). All this is in my area of research - large scale combinatorial optimisation.
Since I don't have a huge amount of time around work/study/gym; I was thinking of setting up a project - perhaps on GitHub - and making it a community project released under GPL. What do you guys think?
