Stop in for a cup of coffee

Explain something to me cuz I'm stoopid!!

If H = T * RPM/5252

Given a torque curve for an engine, one could plot the HP throughout the rpm range...

The math says that torque and horsepower are always equal at 5252 rpm.
And horsepower is always exactly half of torque at 2626 rpm..
.....

So why do I see HP/Torque curves posted that don't follow the laws? Am I missing something?
It's because you aren't using the equation correctly. To determine HP you need to know the torque at a given RPM and then apply the equation to get the HP at that RPM.

Torque at any given rpm does not mean that you can use the equation to calculate the entire torque range unless it is a completely flat or linear curve and you already know what the slope is. The short answer is that the equation is only used to calculate one value from the other (HP or Tq) at any given RPM, not across a range or RPM.

Also, The calculation is for rotating objects and when you look at most dyno sheets they are at the rear wheels and not at the back of the crank which is part of why you see different numbers. The rest is that the internal combustion engine works outside of the basic equation with a dozen other variables that come into play...which is why a vehicle engine can develop 80% of it's peak torque at 1400 rpm.