Calculating max image size for display in an app?

I'm creating a "zoomable" image for use in an iPad app. The PNG is fed into the app via an iframe. It's zoomable because the dimensions stated in the HTML are smaller than the real image dimensions. The person looking at the app uses the "finger spread" method to make the image expand. Sounds odd, but it works. Base image resolution is 264px for retina displays.

Yesterday I tried an image that was 2768 x 4221 pixels and the app simply refused to display it. When I changed it to 1000 x 1525 it displayed fine. Problem is, that should not have worked. Apple says the max pixels for an image on iPad cannot be more than "width x height = 3 x 1024 x 1024" That base formula works out to 3,145,728 pixels. Using Apple's math, my image that displays fine has a total size of 4,575,000.

So I'm confused about how to calculate the correct max image size for these PNGs. Apple's formula looks pretty simple but it didn't work for me. Help?

Message was edited 2/6/2013 by: okieseeker