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Live lab · Visual Geometry

Turn inequalities into pictures you can remember.

Move the construction, see what stays true, then connect the picture back to the algebra.

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One construction. One proof you can move.

The geometry track is intentionally small today: one complete interactive lesson, clearly labeled.

01
Interactive lesson · inequality

See AM-GM inside a semicircle

Move the split point, compare the altitude √ab with the radius (a+b)/2, then find the equality case.

ConstructionAM-GMEquality caseQuick check
How the lab works

Motion first. Proof second.

Instead of beginning with symbolic manipulation, the lesson starts with the invariant picture. The algebra arrives after you have seen what cannot be exceeded.

Move the construction →
  1. 01
    Move the split

    Watch the altitude change while the diameter stays fixed.

  2. 02
    Spot the maximum

    The altitude reaches the radius only at the centered split.

  3. 03
    Name the inequality

    The picture becomes √ab ≤ (a+b)/2.