Prof. Muni Mahendra Kumar
In the above findings, we have assumed the curve to be a conic. This is one possibility. If we can get some more details about the mathematical aspect of the loka, then we could make more precise determination of its shape and dimensions. For example, we have made reference to "vargitaloka" (supra, pp. 141- 143). If we could get exact mathematical connotation of this term, we would be able to find out some way to make a more precise interpretation through the number of khaṇḍukas of vargitaloka which is 15296. We have to make sure as to what exactly this number refers to? Does the surface area of the loka is indicated by vargitaloka? All such questions require a thorough research and precise mathematical interpretation.
Again, it should be noted that so far we have made calculations considering the space to have Euclidean geometry. There seem to be some evidences in the Jain canonical works which tend to show that the actual geometry of the lokākāśa may be a non-Euclidean geometry. One of these evidences is the value of π as accepted in the Jain canonical works. If √10 is actually the value of π, then it shows that the geometry of lokākāśa is non-Euclidean. It is again a matter of further research whether this is only an approximate value used or an actual value based on non-Euclidean geometry. Again, if the shape of the lokākāśa itself is curved then why should we not believe that its geometry is non-Euclidean? If it is really non-Euclidean, then it is required to compute the value of its volume by using non-Euclidean geometry. We may conclude that there is immense scope for further researches in mathematics which is profusely used in Jain canonical and non-canonical works. It may reveal some very important truths which are hitherto not known.
