An equation is something you can play with. Explore a curve, change one assumption, and explain what moved.
Open tools for every maths level. These investigations complement course lessons; they do not turn the levels awaiting materials into complete courses.
MAKE THE MATHS VISIBLE
Your graphing desk.
Choose a starting thought. Predict the graph, then test it.
Launch to load Desmos. Keeping it closed saves memory while you explore the mountain.
THE SYMBOLS SHOULD HELP, NOT GET IN YOUR WAY
A place for the tricky notation.
Fill in the parts, see what they mean, and try the expression in Desmos. Numerical results below are approximate real-number calculations.
log2(8)
logₐ(x) asks: a raised to what power equals x? For example, log₂(8)=3 because 2³=8.
logₐ(x)
Replace 2 with the base, and 8 with the argument. Base > 0, base ≠ 1, argument > 0.
Inside Desmos, open its keypad and functions menu for built-in fractions, radicals, logs, trig, calculus and more. Use ^ for exponents and _ for subscripts. Complex results require its Complex Mode setting.
The standalone root calculation handles odd roots of negative numbers. In Desmos, use the nth-root template for these; fractional powers can follow different real/complex conventions.
Calculator by Desmos Studio. Investigations by Knowledge Mountain. Opening or launching Desmos connects to its service; Desmos privacy policy applies. Knowledge Mountain sign-in does not sign you in to Desmos.
THE MOUNTAIN IS ALWAYS HERE
Mathematics. A mountain of ideas.
27 reading, memory, and recall notes. Repeated cards build the pile; each opens its learning note.
Click a card to unfold it. Drag it onto the desk, then flick and release. Keyboard: Enter opens a card; on a loose note, R returns it. Use Pan view to move across a narrow screen.
THE FIELD DESK / MATHEMATICS
Your notes and learning progress stay safe when the pile moves.
Knowledge MountainA PLACE FOR EVERY CURIOUS MIND