Continued Fractions Sums and Products
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The focus of this project is to study the mathematical relationship of the continued fraction sum and the continuedfraction product. Any real number can be written as a continued fraction, so the addition and multiplication of any two continued fractions is the same as the real numbers they represent. However, the continued fraction sum and continued fraction product each result in another continued fraction. The problem is the determining the relationship that this new continued fraction has with the original two. This will be achieved by observing the characteristics ofthe 3D graphs contained within the unit cube. This topic is interesting because it is relatively unexplored. Whether or not these relationships will lead to anything significant is yet to be determined.