CloudLabs Transform Matrices vs KOURAKU

This situation provides a Cartesian plane where you can draw polygons with up to five sides, which will be represented by matrices. You will be able to configure a transformation matrix in order to operate the matrix that represents the polygon, and then observe the transformation applied to the original polygon.

KOURAKU is a visual education app about how people cross the sea and work out where they are — the science of navigation and positioning — learned by watching and interacting. Follow the story from classical celestial navigation to modern GPS through simulations and hands-on challenges. As the navigation module of the "Raku" series, KOURAKU sits next to KAIRAKU (oceanography). If KAIRAKU is the science of tides and currents, KOURAKU is the craft of using them to cross the ocean. It covers six topics from high-school earth science and physics up to introductory navigation. [Explore and Challenge — a learning cycle] Every mode can be used in two ways: - Explore: move the sliders freely and see the principle at work. - Challenge: solve a task with the answer hidden. Read the instrument to measure, work out your position, then check your answer. When you get it right, the app shows the reasoning step by step. Each mode has 5 stages, for 30 stages across the 6 modes. Cleared stages are recorded in the Logbook on the home screen, so you can see your progress at a glance. [Six Modes] - Celestial Latitude Measure a body's altitude with a sextant and find your latitude. The altitude of Polaris equals your latitude, and from the noon Sun you get latitude = 90° − altitude + declination. In the challenges, line the sextant up with the star or the Sun, read the altitude, and give the ship's latitude. - Longitude & Chronometer Longitude comes from the time difference between local noon and Greenwich time. The Earth turns 15° every hour, so a clock running ahead or behind tells you how far east or west you are. See why a marine chronometer that keeps accurate time at sea made longitude measurable. - Dead Reckoning Build up course and speed over time to estimate your position. Add a current and watch the estimated position drift away from the true one. Challenges range from distance run to choosing a course that allows for the current. - Chart & Compass Correct a compass course for deviation and variation to get the true course (add East, subtract West). Then try the reverse: from a true course on the chart, find the compass course to steer. - Tides The sea rises and falls with the Moon and Sun: spring tides around new and full moon, neap tides around the quarters. Read the times and heights of high and low water from a 24-hour tide curve, and work out when a ship can safely cross a shallow channel. - GPS Positioning Find your position from the distances to several satellites (trilateration). Turn signal travel time into range, see how a tiny receiver clock error throws the fix far off, and how a fourth satellite solves that error. [Features] - 30 challenge stages: 6 modes × 5 stages - A Logbook that records cleared stages (clear it any time) - Principle / explanation sheet in every mode - A one-line "how to try" guide on every screen - A journey through time from classical navigation to modern GPS - 9 languages (Japanese, English, Chinese Simplified/Traditional, Spanish, Portuguese (BR), Korean, German, French) - Supports landscape, large text sizes, and VoiceOver - Difficulty labels (Beginner, Standard, Advanced), a "Start here" mark and a start button on Home show where to begin - Nautical chart and logbook visuals, with dark / light themes - About screen with links to the privacy policy and support - Free to use with every feature unlocked (banner ads only; no in-app purchases or subscriptions) [Recommended for] - Students of earth science, physics, navigation, or positioning - Anyone who wants an intuitive feel for celestial navigation, longitude, and dead reckoning - People interested in the sea, ships, and geography - Teachers looking for classroom material - Anyone curious about how GPS actually works out where you are Note: This app uses simplified simulations for education. Do not use it for real navigation or positioning.