{"id":12,"date":"2026-09-15T20:28:26","date_gmt":"2026-09-15T20:28:26","guid":{"rendered":"https:\/\/siteskite.net\/morphmath-668013\/home\/"},"modified":"2026-09-15T20:28:26","modified_gmt":"2026-09-15T20:28:26","slug":"home","status":"publish","type":"page","link":"https:\/\/siteskite.net\/morphmath-668013\/","title":{"rendered":"Home"},"content":{"rendered":"\n
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Live canvas \u2014 every figure is drawn, not drawn once<\/p>\n\n\n\n

Mathematics you can drag, plot and watch behave.<\/h1>\n\n\n\n

MorphMath Academy turns limits, derivatives and polygons into instruments. Pull a vertex, push a slider, and the measurements recompute in front of you \u2014 then follow the same argument line by line until it clicks.<\/p>\n\n\n\n

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Start lesson<\/a><\/div>\n\n\n\n
Browse the topic library<\/a><\/div>\n<\/div>\n\n\n\n
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18<\/p>\n\n\n\n

interactive labs<\/p>\n<\/div>\n\n\n\n

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150+<\/p>\n\n\n\n

worked solutions<\/p>\n<\/div>\n\n\n\n

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3<\/p>\n\n\n\n

topic tracks<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n

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Morph loop \u2014 move your pointer over the canvas to probe r(\u03b8), perimeter and area.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n

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01 \/ Topic library<\/p>\n\n\n\n

Three tracks, one habit of mind<\/h2>\n\n\n\n

Every topic is taught the same way: build the object, measure it, then write the argument that explains the measurement.<\/p>\n<\/div>\n\n\n\n

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Track 02 \u2014 flagship<\/p>\n\n\n\n

Calculus: limits<\/a><\/h3>\n\n\n\n

Epsilon and delta without the hand-waving. Shrink h, watch the secant slope converge, then squeeze the error below any tolerance you choose.<\/p>\n\n\n\n

31 lessons \u00b7 12 labs<\/p>\n<\/div>\n\n\n\n

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Track 01<\/p>\n\n\n\n

Algebra and functions<\/a><\/h3>\n\n\n\n

Factor, transform and compare functions. Meet slope as a rate of change in the function lab before it ever becomes a formula.<\/p>\n\n\n\n

24 lessons \u00b7 9 labs<\/p>\n<\/div>\n\n\n\n

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Track 03<\/p>\n\n\n\n

Geometry and measurement<\/a><\/h3>\n\n\n\n

Drag a vertex and watch angles, perimeter and area recompute live. Convexity becomes a number you can read, not a shape you guess at.<\/p>\n\n\n\n

19 lessons \u00b7 7 labs<\/p>\n<\/div>\n\n\n\n

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Every track<\/p>\n\n\n\n

Worked solutions<\/a><\/h3>\n\n\n\n

150+ problems solved one line at a time. Amber hints arrive before the answer, never after the deadline.<\/p>\n\n\n\n

Free \u00b7 no account<\/p>\n<\/div>\n<\/div>\n\n\n\n

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Open the topic library<\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n
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02 \/ Interactive labs<\/p>\n\n\n\n

Three tracks, one habit of mind<\/h2>\n\n\n\n

No downloads, no app. Each lab is a small program that draws itself in your browser and answers back the moment you change something.<\/p>\n<\/div>\n\n\n\n

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Lab A \u2014 morph loop<\/p>\n\n\n\n

Morphing geometry<\/h3>\n\n\n\n

A closed curve interpolates between a circle, a square, a triangle, a star and a blob while a probe ray reports r(theta), perimeter and area.<\/p>\n\n\n\n

On the home page \u00b7 always running<\/p>\n<\/div>\n\n\n\n

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Lab B \u2014 five sliders<\/p>\n\n\n\n

Function lab<\/a><\/h3>\n\n\n\n

Move a, b, c, x-zero and h. The curve, the secant through x-zero plus or minus h and the tangent at x-zero all redraw as you drag.<\/p>\n\n\n\n

Calculus \u00b7 20 minutes<\/p>\n<\/div>\n\n\n\n

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Lab C \u2014 drag the vertices<\/p>\n\n\n\n

Polygon lab<\/a><\/h3>\n\n\n\n

Every vertex is draggable. Side lengths, interior angles, the angle sum, area and convexity update on every frame while you pull.<\/p>\n\n\n\n

Geometry \u00b7 15 minutes<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n

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03 \/ Step-by-step solutions<\/p>\n\n\n\n

Limits, line by line<\/h2>\n\n\n\n

A worked solution should read like an argument, not a magic trick. Click once and the next line appears \u2014 with the reason attached to it.<\/p>\n<\/div>\n\n\n\n

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Step 01<\/p>\n\n\n\n

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Read the structure. Substituting x = 2 gives 0\/0, an indeterminate form. That tells you the quotient is undefined at the point \u2014 it says nothing yet about what happens nearby.<\/p>\n<\/div>\n<\/div>\n\n\n\n

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Step 02<\/p>\n\n\n\n

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Factor the numerator. It is a difference of squares, so it splits into two linear factors.<\/p>\n\n\n\n

x\u00b2 \u2212 4 = (x \u2212 2)(x + 2)<\/p>\n<\/div>\n<\/div>\n\n\n\n

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Step 03<\/p>\n\n\n\n

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Cancel the common factor. The cancellation is legal everywhere except the single point you excluded.<\/p>\n\n\n\n

(x\u00b2 \u2212 4) \/ (x \u2212 2) = x + 2,  x \u2260 2<\/p>\n<\/div>\n<\/div>\n\n\n\n

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Step 04<\/p>\n\n\n\n

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Take the limit of the simplified expression. Polynomials are continuous, so substitution \u2014 which failed a moment ago \u2014 now works.<\/p>\n\n\n\n

lim (x \u2192 2) of (x + 2) = 4<\/p>\n<\/div>\n<\/div>\n\n\n\n

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Step 05<\/p>\n\n\n\n

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State the conclusion. The limit is 4 even though f(2) is undefined: a limit is a claim about nearby values, never about the value at the point itself.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n

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lim (x \u2192 2) of (x\u00b2 \u2212 4) \/ (x \u2212 2) = 4<\/p>\n\n\n\n

Stuck at step 2? Ask for the amber hint: it names the algebraic identity to use without handing over the answer.<\/p>\n\n\n\n

How the reveal works<\/h3>\n\n\n\n