Final answer:
A weird-looking cake can be divided into two identical pieces through a single cut by finding a line of symmetry. This might be a straight or curved line that results in two mirror images of each half, reflecting geometric principles of symmetry and congruence.
Step-by-step explanation:
The student's question is about dividing a cake into two exactly alike pieces with a single cut. This falls under Mathematics, specifically geometry, where the concept of symmetry is essential. To divide a weird-looking cake into two identical parts, John should look for a line of symmetry that goes through the cake. This can either be a straight line or a curved line that divides the cake into two mirror images of each other. If the cake is irregular and finding a line of symmetry is challenging, he may have to resort to finding a creative or unusual curved cut guided by the unique shape of the cake.
Another geometrical approach could be to visualize the cake as a 3D object and find a plane that slices the cake into two congruent halves. Often, cakes may be symmetrical across their vertical axis when considering cylindrical or spherical shapes. However, if the cake has a more complex form, the cut might be more intricate and require a more abstract geometrical understanding.