Euclid Lab vs MathBench

Explore the 48 propositions of Book I of Euclid’s Elements through reading, construction and proof practice. Euclid Lab separates proposition reading, straightedge-and-compass work and reasoning so you can focus on one activity at a time. Arrange supplied proof blocks to connect premises to conclusions. Scored exercises use semantic checks of geometric relationships and logical dependencies, not the appearance of a drawing or AI grading. Progressive hints and complete solutions, shown on request, help when you get stuck. I.7 currently offers unscored reading, exploration and notes. Freehand notes are also unscored and are not automatically verified as correct proofs. Foundations and I.1–I.12 are free. I.13–I.24 and I.25–I.48 are separate, one-time in-app purchases. Buying one pack does not unlock the other. No subscription is required. Learning progress and notes are stored locally on your device. Learner profiles are not Apple Accounts, and no Euclid Lab account registration is required. Restore Purchases restores eligible content access; it does not synchronize learning progress.

MathBench turns math into hands-on reasoning. Do the same thing to both sides of a balance until only x remains. Drag parameters until a parabola passes through the target. Bisect an angle with only a compass and straightedge. Every move is checked for equivalence in real time. THREE SUBJECTS, 75 LEVELS Algebra Balance: linear equations, systems, quadratics and inequalities. Multiply by a negative and the sign must flip; divide by an expression in x and you may lose a root. Brainer levels are built around these traps. Graphs: linear, quadratic, inverse and absolute-value functions, shifts and stretches, and solving equations and inequalities by graph. Constructions: perpendicular bisectors, angle bisectors, perpendiculars, parallels, regular hexagons, circumcenter and incenter, tangents to a circle. Each subject has Intro, Core, Brainer and Mixed levels. 30 levels are playable right away; the other 45 unlock with Pro. A daily challenge and a review list bring back levels you solved with help. PRINCIPLE CARDS After each solve, a Principle Card explains why it works using the numbers from your own solve, such as x = (3 ± √17)/4 or 3² + 4² = 25. FIVE TOOLS • Exact fractions: simplify, common denominators, mixed numbers, repeating decimals, prime factorization • Equations: linear and quadratic with exact radicals, inequality intervals, 2×2 and 3×3 linear systems • Graphing: up to three curves with zeros, intersections and vertices • Triangle solver: find the remaining sides, angles and area, including the two-solution case • Statistics: mean, median, mode, range, quartiles, variance and standard deviation, computed exactly as fractions from integers, decimals or fractions Tool results are unlimited; hints are never consumed and undo is unlimited. PRO — ONE-TIME PURCHASE All 75 levels, full Principle Card derivations, step-by-step tool working, and a Free Bench you can edit and save (balance, graph and construction benches). Pro includes every worked answer and all Pro features. The first three fixed sample answers in each subject are free to view; all remaining answers unlock with Pro. One-time purchase. No subscription. PRIVACY All calculations run on your device and work offline. No account and no analytics SDK. Progress syncs through your own private iCloud. NOTE: MathBench is for understanding principles and practicing reasoning. Problems are original, not tied to any textbook, and no exam-score gains are promised. Support, Privacy Policy and Terms of Use are in Settings.