KORAKU vs Linear Algebra

KORAKU is an interactive educational app that visualizes how light behaves in real time. Bend rays with lenses and mirrors, overlap light as a wave, and explore color and photons to connect the equations with what you see. Developer: Fuji Bit Inc. KORAKU is the optics edition of the "-raku" physics simulation series. It turns the optics of school and university physics into moving pictures, not just formulas. 12 simulations in 3 categories: - Rays & Images - Lens: Trace rays through convex and concave lenses. Change the focal length, object distance and height to see the image switch between real and virtual, inverted and upright. Explore 1/f = 1/a + 1/b. - Mirror: Switch between concave and convex mirrors. Move the radius R and object distance a to see how the image changes around the focal point F and center of curvature C, and why a virtual image appears behind the mirror. - Eye & Glasses (new): See the cornea and lens focus an image on the retina. Choose a normal, nearsighted or farsighted eye and change the viewing distance, glasses power (diopters) and accommodation to see where the image forms and how blurry it looks. One tap sets matching glasses. - Prism: Watch white light split into a spectrum. Change the apex angle, angle of incidence and refractive index to see dispersion bend each color differently, with the deviation and minimum deviation. - Optical fiber: See light travel by total internal reflection. Change the launch angle and refractive indices to explore the critical angle, numerical aperture (NA) and when light leaks into the cladding. - Light as a Wave - Diffraction grating: Change the number of slits, spacing and wavelength to find the bright lines at d sin(theta) = m lambda, and watch them sharpen as slits are added. - Thin film: Recreate the colors of soap bubbles and oil films. Change the thickness, refractive index and angle to shift the bright and dark wavelengths. - Polarization: Rotate a polarizer and an analyzer to see Malus's law, I = I0 cos^2(theta): brightest at 0 and 180 degrees, blocked at 90. - Color & the Nature of Light - Color mixing: Compare additive mixing of light (RGB) with subtractive mixing of paint (CMY) using three sliders. - Rainbow: Follow sunlight as it refracts into a raindrop, reflects inside and refracts out. See why the primary bow appears about 42 degrees from the antisolar point, the secondary about 51 degrees, with the colors reversed. - Blue Sky & Sunset (new): See sunlight scattered in the atmosphere. Switch between Rayleigh scattering (proportional to 1/lambda^4) and Mie scattering (cloud droplets, haze), and change the sun altitude and air density. As the air mass grows, the sky and sun turn from daytime blue to sunset colors. - Photoelectric effect: Shine light on a metal and watch electrons fly out. Change the frequency, intensity and work function to explore E = hf, Kmax = hf - W and the threshold frequency f0, with the visible and UV bands marked. Features: - Clean, modern design (dark and light themes) - Home screen organized by category - Tips and a play button in the control panel - Parameter sliders with results that update in real time - Legends and labels for every symbol and colored ray on screen - An explanation sheet with formulas for every simulation - In landscape, the canvas and control panel are shown side by side - Supports larger text sizes - VoiceOver reads out each screen's result (real or virtual image, total internal reflection, and more) - 73 languages including English and Japanese, following your device language - No sign-in: start exploring right away Price: - Free - In-app purchases: none - Subscriptions: none - Ads: a banner ad by Pangle at the bottom of the screen The "-raku" educational app series: - SUUGAKU - Mathematics - BUTURAKU - Mechanics - DENRAKU - Electromagnetism - HARAKU - Waves - KORAKU - Optics

MatrixViz makes linear algebra and computer graphics understandable by turning the maths into interactive visuals. Built for complete beginners, MatrixViz lets you drag vectors, reshape matrices, move cameras, adjust projections, and immediately see what each formula does. Every learning module connects a plain-language idea to a guided experiment, a live visual, the underlying equation, and a symbol-by-symbol explanation. LEARN LINEAR ALGEBRA VISUALLY • Explore vectors in 2D and 3D • Turn matrix columns into draggable handles • See rotation, scale, shear, reflection, and composition happen live • Understand determinants, inverse matrices, span, basis, and independence • Discover eigenvectors by finding the directions a transformation cannot turn UNDERSTAND COMPUTER GRAPHICS • Follow coordinates from object space to the screen • Inspect model, view, and projection matrices • Compare perspective and orthographic projection • Learn cameras, frustums, lighting, normals, depth, blending, winding, and culling • Experiment with Metal shader patterns using beginner-friendly visual controls LEARN BY DOING • Guided lessons paired with the real interactive modules • Always-visible formulas and plain-language symbol keys • Sliders and direct manipulation instead of code-first controls • Saved sandbox presets for returning to experiments • Adaptive layouts for iPhone, iPad, Mac, and Apple Vision Pro • Light and dark appearance options MATRIXVIZ PRO Optional MatrixViz Pro unlocks iCloud lesson-progress sync, educator presentation mode, and 1080p matrix-animation export across supported Apple platforms. MatrixViz Pro Monthly and MatrixViz Pro Yearly are auto-renewable subscriptions. Payment is charged to your Apple Account when the purchase is confirmed. Subscriptions renew automatically unless canceled at least 24 hours before the current period ends. You can manage or cancel subscriptions in Apple Account Settings. MatrixViz Pro Lifetime is a one-time purchase and does not renew. Prices vary by storefront. Privacy Policy: https://docs.google.com/document/d/1pWwcNOmDiuzImLw2JztnpJbhKFnS7unBt5iFSJZcz2w/edit?usp=sharing Terms of Use (Apple Standard EULA): https://www.apple.com/legal/internet-services/itunes/dev/stdeula/ Support: codedspartant@gmail.com