RayLab vs KAKURAKU

RayLab is an application for design and simulation of optics. It can be used either as a learning tool or for the design of real optical systems. Basic version includes: • Ability to model 2D lenses and mirrors • Full control over placement and shape of optical components • Full control over aspheric surface shape parameters • Full geometric ray tracing • Sequential and Non Sequential analysis • Front Focal Length, Back Focal Length, Principle Surface calculations • Sample Models Upgrade to RayLab Pro enables: • 3D Modeling • Advanced Optical Elements such as Lens Arrays, Diffraction Gratings, Prisms, Fresnel Lenses, etc. • Polarization Ray Tracing * Ray Splitting / Beam Splitter modeling • Multi-Configuration Manager and animation functionality • Ability to perform optimizations of design parameters • Ray Transfer Matrix calculation • Various commercial glass catalogs • Zemax Importer • Multiple Analysis Windows: -- Fan Ray Diagram. -- Wavefront Error Plot. -- Grid Distortion Plot. -- Spot Diagram. -- Chromatic Aberration. -- Gaussian Spot Size. -- Polarization Analyzer. Upgrade is available with in-app purchases of various modules OR as a full featured subscription. • The subscription offers a 7 day free trial period. Subscription begins immediately but payment will only be charged to iTunes Account at the end of the trial period. • Subscription automatically renews unless auto-renew is turned off at least 24-hours before the end of the current period. • The account will be charged for renewal within 24-hours prior to the end of the current period, at the same monthly price as the original subscription. • You may manage your subscriptions and auto-renewal may be turned off by going to your iTunes Account Settings after purchase. • No cancellation of the current subscription is allowed during active subscription period. • Any unused portion of a free trial period will be forfeited if the subscription is cancelled. Privacy Policy and Terms of Use: https://www.raymak.com/wp/privacy-policy

KAKURAKU is an educational app that lets you experience probability paradoxes hands-on. Answer with your gut, run the simulation hundreds of times, and compare the result with the mathematical answer. See for yourself where intuition and mathematics part ways. Developer: Fuji Bit Inc. KAKURAKU is the 10th app in the "-raku" series of educational apps, and its theme is probability. It covers 14 famous probability paradoxes, and every one of them unfolds in four phases. Four phases: 1. Gut check: Answer with your intuition first. Most people get these wrong. 2. Simulation: Run one trial at a time or hundreds at once, and see the probabilities as real numbers. 3. The answer: See the mathematical answer and why intuition misses, with diagrams and formulas. 4. Final check: Answer a new question to clear the stage. 14 probability paradoxes in 3 categories: Conditional probability traps - The Door Trap (Monty Hall Problem): Does switching doors win 2/3 of the time? - The Gold Box (Bertrand's Box): Is your 1/2 intuition wrong? - Warden's Verdict (Three Prisoners Problem): Does one word from the warden change A's fate? - Test Trap (False Positive Problem): You test positive, yet the chance you are sick is only 16%? - Sleeping Princess (Sleeping Beauty Problem): 1/2 or 1/3? People still disagree. When statistics fool intuition - Miracle Classroom (Birthday Paradox): With just 23 people, is a shared birthday more likely than not? - Reversed Statistics (Simpson's Paradox): Can the parts and the whole point in opposite directions? - The Endless Bus (Bus Waiting Paradox): Buses come every 10 minutes on average, yet you wait 10 minutes on average? - Red Chain (Gambler's Fallacy): After a run of reds, is black due? - Too Many Ones (Benford's Law) (new): Do about 30% of everyday numbers start with 1? Expected value and decisions - Envelope Dilemma (Two Envelope Problem): Should you keep switching envelopes? - Infinite Gamble (St. Petersburg Paradox): The expected value is infinite, so why would no one pay much to play? - The Predictor's Boxes (Newcomb's Paradox): One box or two? Change the predictor's accuracy and find out. - The Second Mover Wins (Penney's Game) (new): A game of guessing three-coin patterns. Can the second player win up to 7/8 of the time? Features: - Clean, modern design with dark and light themes - Home screen organized by category - Every stage advances in four phases, and you can always see where you are - Graphs and numbers show the results approaching the theoretical value as trials add up - If you go back during the final check, the app asks whether to leave the stage - Available in 73 languages, including English and Japanese (follows your device language) - No sign-in; start right away - Simulations work offline (the network is used only for ads) Great for: - Students learning probability and statistics - Anyone curious about the gap between intuition and mathematics - Teachers looking for classroom material - Anyone who wants to truly understand why the answer is what it is Price and purchases: - Price: Free - In-app purchases: None - Subscriptions: None - Ads: Banner ads by Pangle at the bottom of the screen, and a full-screen (interstitial) ad may be shown when you clear a stage - Ads are personalized only if you allow tracking. You can turn this off in "About this app" > "Ad settings" The "-raku" series of educational apps (selection): - SUUGAKU - Mathematics - BUTURAKU - Mechanics - DENRAKU - Electromagnetism - HARAKU - Waves - NETURAKU - Thermodynamics - KORAKU - Optics - RYURAKU - Fluid dynamics - KAKURAKU - Probability