Plateau's Laws

Bubbles can meet only at Angles of 120° (for two Bubbles) and109.5° (for three Bubbles), where the exact value of 109.5° is theTetrahedral Angle. This was proved by Jean Taylor using Measure Theory to studyArea minimization. The Double Bubble is Area minimizing, but it is not known if the triple Bubble isalso Area minimizing. It is also unknown if empty chambers trapped inside can minimize Area for Bubbles.

References

Morgan, F. ``Mathematicians, including Undergraduates, Look at Soap Bubbles.'' Amer. Math. Monthly 101, 343-351, 1994.

Taylor, J. E. ``The Structure of Singularities in Soap-Bubble-Like and Soap-Film-Like Minimal Surfaces.'' Ann. Math. 103, 489-539, 1976.

• Turán's Inequalities
• Turán's Theorem
• Tutte Polynomial
• Tutte's Graph
• Tutte's Theorem
• Twin Peaks
• Twin Prime Conjecture
• Twin Primes
• Twin Primes Constant
• Twins
• Twirl
• Twist
• Twisted Chevalley Groups
• Twisted Conic
• Twisted Sphere
• Twist Map
• Twist Move
• Twist Number
• Twist-Spun Knot
• Two
• Two-Ears Theorem
• Two-Point Distance
• Two Triangle Theorem
• Tychonof Compactness Theorem
• Type