Ascent: Geometry

Geometry, climbed. Every skill of a full high school Geometry course is a step up the Matterhorn, and reaching the summit means you have finished the course. HOW IT CLIMBS You start in Zermatt and climb the real Hörnli ridge: Furi, Schwarzsee, Hirli, the Hörnli Hut, the Couloirs, the Yellow Band, the Old Hut, the Solvay Hut, the Shoulder, the Fixed Ropes, the Roof, and the summit at 4,478 m. Each landmark is one unit of the course, and every skill you master gains real altitude. Skills are only owned once they stick: spaced reviews come back right before you would forget, and an acclimatization gate at each landmark makes sure the unit below is solid before the next opens. The day follows a real climb: an afternoon approach, sunset at the hut, the lower ridge by headlamp, dawn at the Solvay Hut, and the summit in morning sun. THE ROUTE Tools of geometry. Reasoning and proof. Parallel lines. Transformations. Congruent triangles. Inside triangles: bisectors, midsegments, centroids, the four centers, the triangle inequality. Quadrilaterals and polygons. Similarity. Right triangles and trigonometry. Circles. Coordinate geometry. Area, volume, and surface area. Then Summit Day: three mixed reviews of the whole mountain. Sixty-seven skills in twelve legs. ON THE MOUNTAIN Figures that tell the truth. Every figure is drawn to the measures it states, with tick marks, arcs, right-angle boxes, parallel arrows, circle sectors, dashed hidden edges, solids, and a numbered grid. A magnifier opens any figure full screen. Proofs a phone can do. Two-column proofs are built by tapping statements and reasons. Any valid order passes, the first unsupported step is named, and circular reasoning is caught and explained. Proofs grow with you: reasons first, then ordering, then the whole proof from a bank with distractors. Exact answers. Type 11√3, 7π, or (7, 3) as they are; any correctly simplified form counts. Trig problems print the values you need, so no calculator is required. Stuck never means stranded. The radio to the Hörnli Hut gives four levels of hints on every problem, never punished. Wrong answers are matched against the slips students actually make, like adding the legs instead of their squares, and named with a fix. Every skill has a lesson card with a worked example, and a scratchpad is a tap away for rough work with a finger or Apple Pencil. Route Tests for every leg and a Final Test for the whole mountain, open from day one. A daily Weather Window with its own streak. Expedition patches, a summit certificate to share, and a climber profile for each person on the device. Already partway through Geometry? An optional placement check at the start can move you up the approach as high as the Hörnli Hut. FREE AND PAID, HONESTLY The approach is free forever: legs 1 to 3, from Zermatt to Hirli, with their Route Tests. One purchase, the Full Ascent, opens the climb from the Hörnli Hut to the summit, for every climber profile on the device. No subscription. Family Sharing and Ask to Buy are supported. PRIVATE BY DESIGN No ads, no tracking, no third-party code, no data collection, no account. Everything runs on the device and works offline. EVERY PROBLEM IS REAL MATH Problems, figures, hints, and worked solutions come from our own geometry engine, not from generative AI. Every answer is re-derived independently in our tests, every proof is checked in every valid order, and a teacher read the whole course before release. FOR Students taking or retaking high school Geometry, roughly ages 13 and up, and anyone studying the geometry strand of GCSE, the Australian Curriculum, CBSE, or IGCSE. For Algebra 1, see Ascent: Algebra 1. For ages 8 to 11, see Numina.