This is a humoristic semi-serious treatise on the Trinity from a perspective of mathematical theology. :-) !!

And how could it be otherwise, this one matheological revelation will come to you in three parts. :)

Dedicated to all the great Muslim mathematicians of 
all time  = the past   + the present   + the future!
            [one time]   [another time]  [and one more time]


                   Analogies can be misleading, but they are
                   the least misleading thing that we have.  
                                              Samuel Butler  

1 + 1 + 1 = 1

and then smile and think that is enough to expose the utter craziness of the concept and showing the completely illogical content of the Christian faith.

Now, it seems that the people which use this kind of reasoning are apparently stuck in their preschool education and have never heard that there are other operations one can perform on numbers than just addition.

1 x 1 x 1 = 1

wouldn't lend itself quite as well for the effect those people want to achieve. And the Trinity is a powerful revelation of the Almighty God, so "raising to the power of a number" might be an appropriate 'composition' for relating the 'three Ones' mathematically, which is giving us

  1
 1
1    = 1  

so that we have already a two to one victory over those who have not yet grown out of their restricted imagination of only being able to add numbers. And lest you want to even out the score by pointing to subtraction, think if you want to risk me telling you about division. {Not to mention "extracting first roots", identity mappings, inclusion homomorphisms etc, which are all on my side, but are rated "R" and only allowed for grown-up mathematicians.}

Okay. Having established that mathematics might be able to give more helpful insights into theological concepts, let us explore what else is available. Most readers here are part of an academic community, so I think everyone will able to follow when the level of sophistication increases.

Now the Bible speaks of three "persons" in respect to God. It does not say, the relationship between them is "addition". If we want to use mathematics at all, the question now is: What would be the "Biblically apppropriate, mathematical composition" of the three ones to make another ONE?

But before it becomes more difficult, another easy part. We already have seen that multiplication is a very nice operation. When we venture from mathematics into physics, we win another 'dimension' of thinking since now our numbers come equipped with units and are no longer so shamefully "naked".

So we could write for example:

                                  3
(1 m)  x  (1 m)  x  (1 m)  =  (1 m )

I.e. the product of three times one meter in length, width and height gives us one cubic meter. This "analogy" is not a very good one though, since it would make God, the Father, God, the Son, and God, the Holy Spirit sort of 'the same', since one meter is one meter in whatever direction you measure it. But we can not expect that analogies which are necessarily restricted to your created, material world will be able to perfectly illustrate the nature of the uncreated, spirit being (non-material) of God.

Maybe it would be better to take the physical concept of "force":
[And to pay tribute to our science fiction fans here:]
[ "May the force be with you!"                       ]

                      2                       
(1 kg) x (1 m ) / (1 s ) = 1 N       [i.e. F = m a ]


or the concept of "energy":

             2        2                           2
(1 kg) x (1 m ) / (1 s ) = 1 J       [i.e. E = m c  ]


or "power":

             2        3                         
(1 kg) x (1 m ) / (1 s ) = 1 W    

But that may make the "three different ingredients" a little too different in the end. And none of the individual "parts" IS force. Not the mass, not the length, not the time. But the Biblical revelation insists, that the Father is God, the Son is God and the Holy Spirit is God. But nevertheless, there is only one God(head). I think NO analogy from the created world exists that will ever capture it completely. { But don't say yet, "see, it doesn't work, it is illogical, I knew it all along ..." The best part is still ahead. :) }