Corner pentagon aquariums have two symmetric back walls and a bent viewing panel. The back walls are at 90 degrees to each other and the viewing panel completes the vertical structure. The final assembly consists of a top and a bottom.
The challenge is the short leg dimension of the front viewing panel. A Tenecor® corner pentagon is dimensioned with identical lengths of both the back wall panels and the the distance between the two bends of the viewing panel. The image below represents a 48 x 48 inch pentagon with an identical 48 inch viewing panel. But how did we come up with the 14 inch short leg dimension?
Hello Pythagoras. The Pythagoras theorem is used to find the length of an unknown side and the angle of a triangle. It can also be used in reverse which is what we will be doing.
Let's take a look at that sketch again. The section in blue represents the back walls. Both are 48 inches. The section in red represents the viewing panel. The length between the bends equals the length of the back wall panel. 48=48. Tenecor was the first company to fabricate an acrylic corner pentagon back around 1979. We looked at different designs where the front panel was longer and also where it was shorter, than the back walls. Make the panel longer and you eventually end up with a triangle. Make it shorter and you eventually end up with a square tank. Making them equal turned out to be a nice elegant solution. Ok, back to the math. Notice how the purple lines square up the fabrication to 48x48. They also form a right triangle with the face of the viewing panel. This is where Pythagoras takes over. 48 squared (the face) equals 2,304. This number is equal to squares of both legs depicted by "34". Since both segments are equal, dividing 2,304 by two (1,152) gives you the total for sum of the squares of both. Take the square root of 1,152 and you get 34 (rounded up). The difference between 34 and 48 gives you the short leg dimension (14).