Visual arithmetic, fractions, LCM & HCF, perimeter & area, angles, 2D/3D shapes, trigonometry, algebra proofs, 3D nets, and number series & sequences — pick an operation below and watch every result build up from real, tappable 3D and box diagrams. Drag to orbit, scroll to zoom.
Standard shapes have equal sides (a formula shortcut works) · the Circle is approximated as many tiny straight pieces unrolled into a line · the Irregular L-Shape has six different side lengths, so every side must be added by hand
m and n can be rational (e.g. 0.5, 1.25, 1.5) \u2014 the tile doesn\u2019t have to be a whole-number square
m, n, and o can be rational (e.g. 0.5, 1.25, 1.5) \u2014 the cube doesn\u2019t have to be 1\u00d71\u00d71 \u00b7 for the curved shapes (Sphere, Cone, Cylinder) only whole cubes fully inside are counted, so the count approximates the true volume
Every standard solid starts folded flat as its net — tap "Fold Into 3D Shape" to watch each face hinge up into the solid, or "Flatten Into Net" to unfold it back out. Every face is numbered so you can match it up before and after folding. (A sphere has no true flat net — it's shown as 8 numbered "orange-peel" gores that curl around into the ball, the standard textbook approximation.)
Every step up or down the ladder is \u00d710 \u2014 converting to a smaller unit subdivides the square into little boxes, converting to a larger unit shows one fractional piece of it
Up to 100 people per group · figures spawn on the left (A, pink) and right (B, violet)
Digital
10:10:00 AM
::
drag = orbit · right-click/two-finger drag = pan · scroll = zoom · tap a person for details
JEE Geometry Reference
2D Shapes Gallery
x: 0.0 y: 0.0
zoom: 1.00×
—
Tap a marked point to learn what it is.
45°0.785 rad · Quadrant I
Drag to sweep the angle counter-clockwise from the positive x-axis (0°) all the way to a full turn (360°) — the label beside the circle names the angle type and glows the instant you land exactly on 0°, 90°, 180°, or 360°
62° = 62°
0°
62°
Drag Parallel Lines Tilt to swing BOTH green lines together against the x-axis — they always stay parallel to each other. Drag Transversal Tilt to swing the blue line independently; the highlighted angle pair (pink) updates live to match whichever relationship you pick above
—
Drag the points around the circle — the marked angles update live and the readout confirms the theorem holds for every position you try.
A 50° · B 70° · C 60°
Drag any two angles of the scalene triangle — whichever one you haven't touched most recently locks and auto-adjusts so all three always add up to exactly 180°. Tap "Cut Into Angle Pieces" to slide all three coloured wedges onto one straight line, showing they fit edge to edge into an exact 180° straight angle
A 90° · B 90° · C 90° · D 90°
Drag any three angles of the quadrilateral — whichever one you haven't touched most recently locks and auto-adjusts so all four always add up to exactly 360°. Tap "Cut Into Angle Pieces" to slide all four coloured wedges onto one shared point, showing they fit edge to edge into an exact 360° full turn
A 108° · B 108° · C 108° · D 108° · E 108°
Drag any (sides−1) angles — whichever one you haven't touched most recently locks and auto-adjusts so all angles keep summing to the correct total. Tap "Cut Into Angle Pieces" to converge every coloured wedge onto one shared point
a² = 9 · b² = 16 · c² = 25 (c = 5)
Pick a Pythagorean triple — every option here is an exact whole-number triple, so the tiles always fill the hypotenuse square perfectly. Leg a fills with a red & blue checkerboard, leg b with a classic black & white chess board. Tap "Cut Into Tiles" to fly every tile onto the square outlined in amber on the hypotenuse, proving a² + b² = c²
30°0.524 rad · Quadrant I
Animate P Around Circle
sin θ = 0.500 · cos θ = 0.866
tan θ = 0.577 · sec θ = 1.155
cot θ = 1.732 · csc θ = 2.000
Toggle any function on or off to isolate it. Drag to rotate point P around the unit circle. The vertical tangent line at (1,0) gives tan θ (the cut segment) and sec θ (the slanted radius-line segment); the horizontal tangent line at (0,1) gives cot θ and csc θ the same way. Near 90°/270° the tan/sec line shoots off to infinity (undefined); near 0°/180° the cot/csc line does the same
2x + 3 = 9
Tap "Build Equation" to load it onto the scale.
Colored blocks are the unknown — every block of the same color hides the same weight. Apples are known weights. Tap a block any time to see what it represents. "Next Step" removes equal amounts from both pans (keeping the scale level) until only blocks remain on one side, then splits the apples evenly to reveal the answer.
Show pan weights
LEFT WEIGHT
0
RIGHT WEIGHT
0
Tap "Load Equation" to set a target.
Load an equation, then use the +/− buttons to place that many colored blocks and apples on each pan yourself — matching exactly what the equation says belongs on the left and on the right. Get every count right on both sides to complete it.
🔒 Secret weights hidden
Add blocks to each pan and watch it tilt.
Each x/y/z block hides a fixed secret weight; every apple (known weight) is worth exactly 1. Mix any combination on either pan — the scale tilts toward the heavier side for real. Tap "Reveal Weights" once you've made your prediction.
Volume
—
Equivalent
—
✓ Volumes match exactly
The cyan solid keeps its own independent dimensions; the amber cuboid is built to hold exactly the same volume. A sphere (1 variable) becomes a cube. A cylinder or cone (2 variables) becomes a square-base cuboid \u2014 you set the base side, the height is solved for. A frustum (3 variables) becomes a general cuboid \u2014 you set the length and width, the height is solved for.
Tap 2 points to use the ruler.
1.0×
Controls how gradually the √ Spiral, Angle, and Perpendicular Bisector presets below draw each step — slide left for slow motion, right to speed the construction up.
Animates the Spiral of Theodorus: each right triangle adds a perpendicular unit leg, so its hypotenuse grows 1→√2→√3→√4→√5 by Pythagoras — the compass then swings that exact hypotenuse down onto the number line to mark the point.
Pure ruler-and-compass construction: swing radius r from O to get 60° (equilateral triangle), repeat from that point for 120°, then bisect (equal arcs from both rays) for 90°, 45°, and 30° — no protractor used.
For a given segment AB: equal-radius arcs (radius > half of AB) centred at A and centred at B cross at two points above and below the line; joining those two points draws the perpendicular bisector, and where it crosses AB is the exact midpoint M.
::
10:10:00 AM
Live Time follows the real clock, seconds hand and all. Custom lets you set any hour/minute/second, then Run to watch it tick forward from there, or leave it paused to study one fixed moment. The digital display beside the clock has its own matching Live/Custom controls too, so it can be set independently right there.
90°mirror tilt from horizontal
Does it match?
Pick a digit or letter and watch its mirror image appear on the far side of the dashed mirror line. Drag the slider (or use the Vertical/Horizontal buttons) to tilt the mirror itself — some characters look identical to their reflection only at certain tilts, which is exactly what "line symmetry" means.
0°
Step 0 / 3
Min. Angle
120°
Order
3
The Free Rotation slider spins the shape by any amount. The Snap slider jumps only between the shape's own symmetry positions — each of the n steps rotates by exactly 360°/n, so the labelled outline lands back on an identical-looking copy of itself every time.
A hidden rule links the teacher (cyan) and student (orange) triangles. Read the marked sides/angles, then match them.
Adjust the student triangle to match the marked measurements.
Teacher (cyan)
Student (orange)
Every slider is always visible for both triangles, but only 3 of the 6 measurements matter for the hidden rule — the marked arcs/ticks (and right-angle bracket for RHS) on both triangles show which ones. Moving a side slider sets that length directly; moving an angle slider keeps its two adjacent sides fixed and solves the opposite side, so every position is always a valid triangle.