This release completes the analytic-geometry side of the app: conic sections you can insert, inspect and reshape with sliders, plus line-conic intersections, a function-properties card, and one-tap Clear Notes. NEW · CONIC SECTIONS · Insert an ellipse, hyperbola or parabola from the Curves panel · Set the centre or vertex, a / b / p, the focus axis or opening direction, with a live preview of the standard equation · Select a conic to see its equation, foci, vertices, semi-axes, eccentricity, asymptotes, directrix and latus rectum · Drag a / b / p with the parameter slider and watch the curve change · Both branches of a hyperbola move together and are removed by a single undo · Conics are included in PDF / PNG export, not just on screen NEW · LINE × CONIC INTERSECTIONS · Mark a conic, then select a line to intersect it; the reverse direction works too · The discriminant and the number of intersections are shown: two points, a tangent, or none · With two points you also get the chord length and midpoint, marked on the graph · This sits alongside the existing function × function intersection, and says so plainly when a pair is not supported yet NEW · FUNCTION PROPERTIES · Select a function curve to read its domain, range, parity, period, monotonic intervals, extrema and asymptotes · Periodic functions are shown over several periods near the origin, with a note when the scan is limited · Values are spelled exactly with π, radicals and fractions, and can be copied as text NEW · PARAMETER SLIDERS · Drag a / b / c on a quadratic, A / ω on a trig function, the base of an exponential or logarithm, or the exponent of a power · The curve updates live; the whole session becomes one undo step · Type an exact value, reset, or cancel; conics use the same slider card NEW · EQUATION CARDS · Select a line to see its equation and angle of inclination · Select a circle to see its standard form, general form and radius NEW · CLEAR NOTES · New "Clear Notes" item in the top-right menu · Clear the current page or all pages, and choose ink, shapes (including tables and sticky notes) or images · Undo restores everything; backgrounds and saved snapshots are left alone FIXES & POLISH · Curves now stop at the coordinate-system frame instead of running past it · Sticky-note ink is saved reliably and undo matches what you see, including lasso in scroll mode · The ink commit path was reworked to avoid needless view rebuilds, for steadier pen response · New Feedback entry in the menu · General stability fixes GOOD FOR · Teaching conics: drag a / b / p and turn "a larger ellipse is flatter" into something visible · Analytic-geometry homework: check intersections, chord length and midpoint on the spot · Function revision: domain, range, parity, monotonicity and extrema in one card · Lesson prep: export curves, equations and labels together as PDF / PNG

This update is focused on fixes and polish, and it brings the everyday math tools together in one place. FIXES & POLISH · Calligraphy brush previews as you write — the stroke no longer waits until you lift the pen · Fast, continuous writing keeps every stroke; no more missing ink · Switching tools no longer changes the thickness of strokes you already drew · A cleaner eraser: erased strokes stay erased when you draw again, and neighbouring strokes are left untouched · General stability and responsiveness improvements NEW · MATH TOOLS · Calculator — one tap from the top-right menu, with parentheses, sign and decimals; copy the result · Is it prime? — a clear yes or no, plus how far the divisors were checked and what divides it · Prime factorization — break any whole number down, with the number of divisors · Factor a polynomial — multivariable polynomials too: x^2 - y^2, x^3 - 6x^2 + 11x - 6, 3x^3 - y^3 · Divisors — every divisor listed, with the count and their sum · Remainder — quotient and remainder together, with the textbook sign convention · GCD / LCM — several integers at once, plus a coprime check · Number base — decimal to binary, octal or hex · Quadratic equation — discriminant D = b^2 - 4ac, the nature of the roots and exact solutions; "no real roots" when that is the answer NEW · FUNCTION DOMAIN · Limit the universal function builder to an interval for x, with the effective domain and range shown live GOOD FOR · Quick checks in class, and factoring on the spot while you explain · Students checking their own work: primes, divisors and equations in one place · Building factorable polynomials when you prepare a lesson

GeomNotes is a notebook with a geometry set built in: you write by hand, and the figures you draw come out exact. Ink and shapes live in separate layers, so handwriting always stays readable on top of the diagram. This release adds curve analysis. Select a curve and you can get its derivative, draw a tangent line, and find its zeros and its intersections — each one labelled on the graph. ANALYZE A CURVE · Derivative f'(x) — select a curve and tap once. No dialog, no typing. The derived curve is inserted and selected for you. · Tangent line — type the tangent point x0 as a decimal, a fraction such as 1/2, or a multiple of π. f(x0), f'(x0) and the tangent equation update as you type. · Zeros — every zero is marked on the curve and listed for you. Exact values read "x = π/2" or "x = 1/3"; approximate ones read "x ≈ 1.7321". An approximation is never written as an equality. · Intersections — mark one curve as "Curve 1", select a second one, then choose "Intersect with Curve 1". Every crossing point is labelled with its coordinates. · Inverse functions — reflect a curve about y = x, with an automatic one-to-one check and branch selection for functions that are not monotonic. · Clear marks — remove every zero and intersection marker from a curve in one tap. · It all cascades: delete the original curve and its derivative, tangents and markers go with it. Nothing is left stranded on the canvas. FUNCTION GRAPHING · A universal builder: x^α, b^x, log_b x, sin(ωx), cos(ωx), tan(ωx). Combine any number of terms to plot polynomials and composite functions. · Every term has an "Applies to" field, so a kernel can act on an expression instead of only on x — a sine term becomes y = sin(2x + 1), a log term becomes y = ln(x - 1). · Bases e, 2, 10 or custom; ω accepts 1, 2, π/2, π, 2π and more. · Live preview while you type, and new curves match the scale and rotation of the coordinate system they are drawn into. · One-tap linear, quadratic and reciprocal graphs. GEOMETRY · Ruler, set square, protractor and compass. · Regular polygons: set the number of edges, drag a vertex, and get an exact figure. · Coordinate systems with zoom, rotation, a custom unit per grid, and tick labels that read as multiples of π — the period of y = sin x finally lands on the grid. · Editing a system you already inserted no longer means inserting a second one. Select the axes, tap "Edit Coordinate System", and the zoom, rotation, units and tick labels are updated in place. HANDWRITING · Fountain pen, pencil, brush, watercolor and charcoal, with pressure and tilt response. · An ink-aware eraser that removes a stroke without damaging its neighbours. · Works with finger and with Apple Pencil. PDF AND DOCUMENTS · Import PDFs and images and annotate them directly. · Pixel Copy: select any region to get a PNG on your clipboard and inserted as an editable image — handy for building worksheet templates. · A built-in table tool for quick data capture in class. · Sticky notes, shapes and images, each in its own toggleable layer. · Multi-page documents with thumbnail navigation, plus a built-in timer. EXPORT AND SHARE · Export to PDF or PNG and share through the system share sheet. GOOD FOR · Teaching monotonicity and extrema — put f and f' in the same coordinate system and "f' > 0 exactly where f is rising" stops being a sentence to memorise · Marking homework — zeros and intersections found and labelled for you · Trigonometry — π ticks put the period on the grid · Lesson prep — export a clean graph straight to PDF Core handwriting is free. Pro unlocks advanced geometry tools, function graphing, curve analysis and inverse functions, and high-quality export.

本次更新为「函数」能力带来一次大升级，手写笔记与数学作图现在可以无缝衔接。 【新增 · 万能函数工具】 · 幂函数：内置 1、2、3、4、5、6、1/2、1/3、-1、-2、-3 等预设指数，也可输入任意实数 · 指数函数：底数支持 e、2、10 及自定义 · 对数函数 l：支持 ln（自然对数）、lg（常用对数）及自定义底数 · 三角函数 sin(x)、cos(x)、tan(x) · 任意项数自由组合、逐项相加：多项式、指数型、对数型、三角型函数都能一次画成 · 输入即实时预览，插入后自动对齐当前坐标系的缩放与旋转 【新增 · 反函数】 · 选中任意已绘制曲线即可「求反函数」，一键得到关于 y = x 对称的图像 · 自动判断是否一一对应；非单调函数可选择反函数分支 · 可选绘制虚线对称轴 y = x，并保留原函数，便于对照讲解 · 支持幂、指数、对数、线性等常见函数的精确反演 【新增 · 坐标系快速插入】 · 绘制一次函数、二次函数、反比例函数或任意函数图像前，若画布尚无坐标系，会直接提示一键「添加坐标系」，不再中断作图思路 【改进】 · 函数工具入口重新整合：坐标系与基础函数、函数族、万能函数统一收纳在「函数」面板中，工具栏更清爽 · 修复试用期间部分权益被误判为已过期的问题，试用体验更稳定 【适用场景】 · 高中函数教学与作业：指数、对数、幂函数图像与反函数对称性一目了然 · 课堂演示：现场画图、现场变式，配合手写批注同步讲解 · 讲义备课：精确的函数图像可直接导出 PDF / PNG