Class 6 • Interactive Geometry and Number Sequence Lab
exploreSlide the controllers below to visually merge two consecutive triangular numbers into a perfect square number!
tune Pattern Dimensions
Configure the size ($n$) of the square grid matrix.
Base Pattern Size (n)4
Tactile Merge Slider0%
Slide right to watch the consecutive triangles assemble into a perfect square!
The Relationship Rule:
Adding two consecutive triangular numbers always yields a square number:
Tn-1 + Tn = n²
Tn (Amber/Teal First Group) Tn-1 (Rose Second Group)
T₃ + T₄ = 6 + 10 = 16 (4² Square)
Slide the controller above to merge a triangular block of 6 rose dots with 10 teal dots.
grain Graph Node Settings
Configure vertices (dots) to see connection counts.
Number of Vertices (V)5
Geometry to Number Rule:
In a fully-connected shape network, the number of lines (edges) is always equal to the $(V-1)^{\text{th}}$ Triangular Number!
Edges = V × (V - 1) / 2
💡 Interactive: Hover over or tap any vertex dot to highlight its specific connecting lines!
Vertices: 5 • Edges: 10
A pentagon with all diagonals drawn has 10 lines. Notice that 10 is the 4th Triangular Number!
pattern Virahānka Sequences
Explore the standard pattern sequence: $1, 2, 3, 5, 8, 13, 21, \dots$
Sequence Generation Step5 (Value: 8)
Visual Overlays
Traditional AP Context:
Traditional threshold-drawings (Muggulu/Sankranti muggu) use recursive, symmetrical loop patterns drawn around a set of lattice points, mimicking mathematics sequences perfectly!
💡 Each square's side length is the sum of the previous two squares' side lengths!
1, 2, 3, 5, 8
The current Virahānka number sequence is: 1, 2, 3, 5, 8. Sum rule: 3 + 5 = 8.