datapad.tools

Math Board is an online whiteboard for maths teachers. With these tools you make a board (for example, a step-by-step solution of a problem) and give the user a link that opens it in their browser. No sign-in is needed. How to make a board: 1. Write the board text in the Math Board format (call get_board_format if you do not have it). 2. Call check_board with the whole text. Fix every ERROR it reports and check again. 3. Call publish_board with the whole text. Give the user the link it returns. Check the mathematics yourself as well: a teacher will show the board to students. When the user gives you a Math Board link (.../live/... or .../s/...#...), call read_board with it to see the board. A live link is the board the teacher has open now: add to it with add_to_board (check_board first), and the teacher sees the addition at once. MATH BOARD FORMAT Write the whole board as ONE code block: the first line is ~~~mathboard and the last line is ~~~. Write nothing else inside it. Inside the block, use Markdown: # Board title (once, on the first line) ## Page name (starts a new page; at most 40 characters) ### Heading (a heading on the page) Paragraphs, **bold**, *italic*, lists (- item, 1. item), > notes, tables (| a | b |), and --- for a line across. Formulas are LaTeX: $x^2 + 1$ among the words, and $$\frac{a+b}{2}$$ on a line of its own. Pictures go in blocks that start with :::graph, :::geometry or :::solid on a line of their own and end with ::: on a line of its own. Never use backticks inside the board: the board must stay ONE code block. :::graph x: -2..6 y: -2..5 y = x^2 - 4*x + 3 y = a*x - 1 a = 0.5 (-2..2) (2, -1) ::: In a graph: optional x and y ranges (the y range is found when left out), then one curve per line: y = f(x), x = number, or a point (a, b). Use x, numbers, + - * / ^, sqrt, abs, sin, cos, tan, ln, log, exp, pi, and letters defined as sliders: "a = 0.5 (-2..2)". :::geometry A = (0, 0) B = (6, 0) C = (2, 4) triangle A B C H = foot C A B segment C H dashed angle C H B right segment A B "6 cm" M = midpoint A C segment B M ticks=1 angle B A C "α" ::: In geometry: points with coordinates (y goes up; the drawing is scaled to fit), then what to draw: segment A B, line A B, triangle A B C, polygon A B C D, circle O A (centre O through A), circumcircle A B C, incircle A B C, M = midpoint A B, H = foot C A B (foot of the perpendicular from C to line AB), L = bisector C A B (where the bisector of the angle at C meets AB), P = intersection A B C D (lines AB and CD, drawn first), D = on A B 0.3 (on segment AB), O = center circumcircle A B C, angle A B C right, angle A B C "60°", angle A B C measured, angle A B C arcs=2 (equal angles: 1 to 3 arcs; B is the vertex). After a line or a figure: "label" in quotes, ticks=1 (equal-side marks 1 to 3), dashed or dotted, color=red, hand (drawn as by hand). "K = (1, 2) hidden" is a point with no dot and no name. Write "hand" after the block type (:::geometry hand) to draw every line of the picture as by hand, as a teacher draws on the board. Space geometry is drawn as in a textbook, with the coordinates of the picture: a plane is a parallelogram, "plane α" and three of its corners in order; hidden lines are dashed. A point at the same fraction along AB and AB1 makes CC1 parallel to BB1. :::geometry plane α (0, 0) (8, 0) (10, 3) A = (2.5, 1.2) B = (5.5, 6.5) B1 = (8, 1.6) segment A B segment A B1 segment B B1 C = on A B 0.5 C1 = on A B1 0.5 segment C C1 ::: :::solid cone ::: A solid: cube, cuboid, prism3, prism4, pyramid3, pyramid4, cylinder, cone, frustum, sphere or hemisphere; add "oblique" for the textbook view, and "hand" to draw it as by hand. Write "right" after the type of a block (:::geometry right) to put the picture to the right of the text before it. RULES - Put everything on ONE page, unless the request asks for more pages. Use ### headings for the steps. - Put a graph or a drawing right after the step it belongs to, with "right". - Check every number and every step. The teacher will show the board to students. - No images, no HTML, no other block types. EXAMPLE ~~~mathboard # Quadratic equation ## Solution ### Problem Solve the equation $x^2 - 5x + 6 = 0$. ### Step 1. Discriminant For $ax^2 + bx + c = 0$: $a = 1$, $b = -5$, $c = 6$. $$D = b^2 - 4ac = 25 - 24 = 1$$ **D > 0**, so there are two roots. ### Step 2. Roots $$x_{1,2} = \frac{-b \pm \sqrt{D}}{2a} = \frac{5 \pm 1}{2}$$ - $x_1 = 3$ - $x_2 = 2$ :::graph right x: -1..5 y = x^2 - 5*x + 6 (2, 0) (3, 0) ::: ### Answer > **Answer:** $x_1 = 2$, $x_2 = 3$. ~~~