MaplePrimes - Maplesoft Blog

Because $F17*(1+$B$4)^3 is not Engineering Documentation

Samir Khan — Thu, 23 Jul 2026 19:37:05 Z

We’ve just launched Maple Flow 2026. And yes, the title of this post doesn’t follow the standard formula for a “new version, new features” announcement.

But this is not only a post about a new version number and new features.

It is about a problem engineers know too well: important calculations trapped inside spreadsheets, scripts and old project files - visible only as cell references, code fragments and hidden logic.

That might be fine when the calculation is being built. It is not fine when the calculation must be reviewed, reused, defended, audited or handed to another engineer.

Maple Flow is built around a simple idea: engineering calculations should be readable, structured, auditable and easy to share.

The new release gives engineers better ways to create those calculations, bring existing work into Maple Flow, and turn legacy material into documentation that actually explains the engineering.

You can now generate Maple Flow worksheets using tools like Codex or Claude Code. This makes it easier to transform ideas into structured technical analyses and turn existing calculations into clear, auditable engineering documents.

Here are a few ways to use this new integration,

Rescue calculations from spreadsheets

Many engineering teams have years - sometimes decades - of calculations sitting in Excel. Those spreadsheets often contain real engineering value, but the logic is fragmented across cells, sheets and references.

Manually translating all that work into a clearer format can feel like too much effort to even start.

With Maple Flow 2026 and an AI coding assistant such as Codex or Claude Code, you can use a simple instruction like:

Convert this Excel spreadsheet to a Maple Flow worksheet

The AI coding assistant then helps transform spreadsheet logic into a structured Maple Flow worksheet with natural 2D math, clearer variable names and calculations that are visible on the page.

This is not just file conversion. It is a way to expose the engineering intent hidden inside legacy spreadsheets and make that work easier to understand, extend and review.

Generate engineering worksheets from a prompt

The same AI-assisted workflow can also help create a new Maple Flow worksheet from a natural language prompt.

Ask for a design calculation, describe the engineering context, specify the assumptions and ask for supporting text, equations, plots or diagrams. The result can be a worksheet that already contains readable math, explanations and visual context.

Stop hiding math in scripts

Maple Flow 2026 also opens up a practical path for moving useful work out of scripts and into worksheets that communicate the engineering more clearly.

For example, a Matlab script built around low-level loops, switch/case logic and numerical iteration can be translated into a Maple Flow worksheet that uses higher-level mathematical constructs.

In one example, a crude while-loop numerical solver became an fsolve call, and switch/case logic became a much more readable piecewise expression.

The point is not simply to change syntax. It is to move from code that performs a calculation to a worksheet that explains the calculation.

I've outlined a few ideas that demonstrate how you can use AI coding assistants to generate Maple Flow worksheets. There's much more you can do.

Of course, this functionality is subject to the same disclaimers as any other AI-generated content:

Worksheets are generated by and subject to the limitations of your AI model
your mileage may vary
and you absolutely need a (human) expert in the loop to check the output.

But as a starting point, this workflow is seriously powerful.

Set up your AI coding assistant to generate Maple Flow worksheets with the instructions here.

Maple Flow 2026 introduces in-worksheet programming, so you can write programs and scripts directly on the canvas and execute them inline with the rest of your worksheet.

You can enter programs with the keyboard or use the new Programming palette, which inserts common templates such as loops and if/else blocks with the right structure and indentation.

Productivity features help keep the program readable:

automatic closing of procedures, loops and conditionals after the opening line is entered
intelligent insertion of statement separators when appropriate
automatic indentation to preserve structure and readability

The existing Code Editor remains the right place for larger scripts. In-worksheet programming is for the logic you want to sit directly beside the math, text and results.

The Mathcad Migration Assistant has also been updated. It now translates much of the content of Mathcad Prime files into Maple Flow format, in addition to the existing support for Mathcad 13, 14 and 15.

Because Maple Flow 2026 now supports in-worksheet programming, the updated Migration Assistant also translates Mathcad programs.

For Mathcad thinking about moving to Maple Flow, the update makes migration faster and more practical. Existing work moves over with more of the structure and intent preserved.

Worksheets now compute faster! The results depend on the specific calculations, but the improvements can be very noticable - these are selected results from our internal benchmarking suite

For engineers working with larger or more complex worksheets, that kind of improvement changes the feel of the product.

Maple Flow 2026 adds more ready-to-use examples to the Application Gallery, including a new Semiconductor section.

The gallery now includes worksheets semiconductor oxide growth, heat sink sizing, cylindrical fin heat transfer, NMOS threshold voltage, MOSFET power loss, photolithography scanner limits and boron implantation stability.

Maple Flow 2026 also improves everyday interoperability with Excel. You can now paste more types of data from Excel into Maple Flow, including data formatted as percentages.

It is a small feature with a practical benefit: less cleanup, fewer interruptions and a smoother path from spreadsheet data to engineering calculation.

The most important thing about Maple Flow 2026 is not any single feature - it is the direction of travel. Engineering work is becoming more connected. Calculations are moving between spreadsheets, scripts, AI coding assistants, design tools and formal documentation.

Maple Flow gives those calculations a place where the math is visible, the structure is clear and the result is ready to share.

So yes, Maple Flow 2026 includes new features. But the bigger story is this: engineers can now move more of their existing work out of hidden logic and into auditable worksheets that communicate the engineering.

Explore the new features, try the examples and experiment with generating worksheets using AI coding assistants. Grab a trial here.

Math Success in the Age of AI: Introducing the Maplesoft Math Success Platform

Karishma — Thu, 02 Jul 2026 19:06:37 Z

Last week, we launched the Maplesoft Math Success Platform.

This launch reflects a lot of conversations I’ve had over the past year with educators and institutions about what it means to teach and learn math in the age of AI.

At first, many of those conversations were about visibility. If students were completing homework, quizzes, and other assessments with help from AI, those results became harder to interpret. Did students understand the work, or had they copied down a solution that made sense in the moment without building the understanding needed to do something similar on their own?

That visibility still matters.

Over time, though, those conversations led to a more nuanced conclusion. The question is not simply how we prevent students from taking shortcuts. It is how we help them develop the mathematical judgment, intuition, and critical thinking they will need in a world where AI is part of how they learn and work.

In some ways, that has become even more important. When answers are easy to generate, students need to be able to test ideas, recognize when something does not make sense, explain their reasoning, and trust their own thinking.

That is why I am proud to share the launch of the Maplesoft Math Success Platform.

Built on Maple, the platform brings together our math technology and extends it with analytics, AI-driven insights, targeted resources, and content expertise to help institutions support math learning in a more complete way.

It gives instructors and learning support teams better insight into where students are struggling, supports the creation of better questions and learning experiences, helps students move beyond the answer, and helps institutions respond to a world where AI is now part of how students practice, study, and get help.

You can learn more about the Maplesoft Math Success Platform on our website.

We also wrote more about the thinking behind this launch in our new whitepaper, Math Education in the Age of AI: From Grading Answers to Understanding Student Progress. It looks at why math education needs a new approach in the age of AI: one that helps instructors ask better questions, create learning experiences that build understanding, and use learning signals to see where students need support.

I’d love to hear what you think. How are you seeing AI change the way students learn, practice, and get help in math? And what kinds of tools or approaches do you think will be most important as math education continues to evolve?

Animating a Polyhedron

pchin — Tue, 09 Jun 2026 13:32:04 Z

A little while ago, I created a video, Engaging and Enlightening Students with Maple Visualizations, that showed a sample of Maple visualizations that would be helpful in teaching math. Doing that allowed me to get reacquainted with some of Maple's plotting features that I hadn't used for a while. As a result, I made a second instructional video for my Maple tips series, Animating a Polyhedron in Maple.

I chose this topic because I thought it would show several features in Maple that might not be known to all users. I list them below and encourage you to try them out.

The plots:-polyhedraplot command allows you to create a 3-D plot of a polyhedron, including one of 138 polyhedra that Maple knows about.
The list of named polyhedra available can be obtained by calling the plots:-polyhedra_supported command.
The viewpoint option, which allows you to create an animation by varying the viewpoint through a 3D plot, can be used to rotate the polyhedron.
Finally, the Export feature allows you to save the plot animation as an animated GIF.

New Maple Videos

pchin — Wed, 06 May 2026 15:12:24 Z

Over the past few months, I've created a number of short videos. My intention is to help people use Maple more effectively. I occasionally give workshops introducing Maple and its programming language, and many of the topics come from questions I get from the participants.

These can be found on our Youtube channel. Here are the ones posted so far.

What is a Workbook?
Creating a Workbook
How to Customize Your Maple Settings with the Options Dialog
What is Maple Transactions?
How to Submit an Article to Maple Transactions
Quotation Marks in Maple
Using Single Quotes to Prevent Evaluation

If you find these helpful and have suggestions for future videos, please leave a comment, thanks!

Estimating Pi Using Randomness - Buffon's Needle

callumneily — Tue, 24 Mar 2026 17:59:57 Z

Mathematics often feels precise and deterministic. We solve equations, follow logical steps, and do our best to arrive at exact answers. But sometimes, surprisingly, randomness can also lead us to deep mathematical truths. One of the most famous examples of this idea is a problem from the 18th century known as Buffon’s Needle.

Imagine you have a floor made of long wooden planks placed side by side. The seams between the planks form a set of equally spaced parallel lines across the floor. Now, suppose you take a needle and randomly drop it onto the floor. Sometimes the needle lands entirely on one plank. Other times, it crosses one of the seams between planks, as shown below.

Now here is the curious question posed by the French mathematician Georges-Louis Leclerc, Comte de Buffon in the 1700s:

If we repeatedly drop the needle at random, what is the probability that it crosses one of the lines on the floor?

At first glance, this sounds like a simple probability puzzle. But the answer turns out to involve one of the most famous numbers in mathematics: π.

To keep things simple, assume the distance between the parallel lines on the floor is the same as the length of the needle. We can also imagine that all of our needles are thrown onto the same plank, potentially crossing onto the plank above or below. This configuration is equivalent to throwing the needle onto any plank as long as the planks are equally wide; this modification makes the analysis much simpler.

Every time the needle lands, two things determine whether it crosses a line:

The distance x from the center of the needle to the nearest line
The angle θ at which the needle lands with respect to the parallel lines

See a depiction of this below.

To determine the probability of a needle crossing one of these lines, we need to describe what a "random drop" of the needle means mathematically. If the lines are the same length apart as the length of the needle L, then the center of the needle can never be farther than L/2 from the nearest line. Therefore, 0 ≤ x ≤ L/2. Next, we can simplify our domain for θ. The problem is symmetric, so we only need to consider angles between 0 and π/2. Any given half of the needle then has a vertical reach of (L/2)sin(θ).

We will say a needle "crosses" a line precisely when the center lands close enough to a line that one end of the needle can reach across the line. This occurs when x ≤ (L/2)sin(θ).

An important assumption to make is that every pair (x,θ) in the rectangle 0 ≤ x ≤L/2, 0 ≤ θ ≤ π/2 is equally likely. We’re assuming the needle lands with uniform randomness over all vertical positions x and angles θ. This means that the probability of crossing a line is the fraction of this region where the inequalities above hold. That is,

Probability = (area of favourable region) / (area of total region)

The "rectangle" formed by inequalities has a total area of (L/2) * (π/2) = π*L/4. The needle crosses a line exactly when x ≤ (L/2)sin(θ), so for a fixed angle θ, the allowable x values are 0 ≤ x ≤ (L/2)sin(θ). The favourable area is then:

The probability of a needle crossing a line is therefore:

This result leads to a fascinating idea. If the probability of crossing a line is 2/π, we can rearrange the formula to estimate π itself:

π ≈ 2N / C

where:

N = the total number of needle drops
C = the number of times the needle crosses a line

In other words, by performing a simple random experiment and counting how often the needle crosses a line, we can approximate π.

For example, suppose you drop the needle 10,000 times and it crosses a line 6,366 times. Plugging these values into the formula gives

π ≈ (2 × 10,000) / 6,366 ≈ 3.14

With enough trials, the estimate tends to get closer and closer to the true value of π. At the bottom of this post, I attached a Maple worksheet that simulates this phenomenon. Below are results from simulating this result using N = 10, 100 & 1000, respectively. Notice as N increases, our approximation for π tends to become more and more accurate.

Below is a more dynamic simulation from the Maple worksheet to show how the approximation stabilizes as N increases.

What makes Buffon’s Needle so fascinating is the unexpected connection between geometry, probability, and one of mathematics’ most important constants.

π usually appears when dealing with circles (circumference, area, rotation, etc). But in Buffon’s experiment, there are no circles at all. Instead, π emerges from the geometry of all the possible ways a needle can land on a set of parallel lines.

This was one of the earliest examples of what we now call a Monte Carlo method, which is essentially using random experiments to estimate numerical values. Today, similar techniques are used in physics, finance, computer graphics, and machine learning.

One of the best parts of Buffon’s Needle is that you can try it yourself. All you need is:

A toothpick or needle
A piece of paper with a sequence of parallel lines, each a distance of the needle's length apart
A lot of patience

Drop the needle repeatedly (N times), record how many times it crosses a line (C), and compute 2N/C. The more times you repeat the experiment, the closer your estimate will get to π.

After reading about this experiment, I was convinced that mathematics is not only about abstract symbols and formulas. Sometimes, even something as simple as dropping a needle onto the floor can reveal the hidden structure of elements of the universe that we would've otherwise never known were there.

Buffons_Needle_Simulation.mw

Gabriel's Horn

callumneily — Tue, 17 Mar 2026 16:15:31 Z

Gabriel’s Horn is one of the most famous examples in calculus of how infinity can behave in ways that completely defy our intuition.

The horn-shaped object is created from a very simple curve: y = 1/x for x ≥ 1 (pictured below).

Now imagine rotating this curve around the x-axis. The resulting surface stretches infinitely far to the right while becoming thinner and thinner. Visually, it resembles a long trumpet or horn that continuously narrows to a thickness of zero.

At first glance, nothing about this shape seems particularly mysterious. As x grows larger, the radius 1/x becomes smaller and smaller. It seems reasonable that both the volume contained inside the horn and the area of its surface would remain finite (or at least if the volume was finite, then the surface area would also be finite). After all, the horn gets extremely thin very quickly.

Calculus allows us to test that intuition.

To compute the volume of the horn, we use the disk method. Each slice perpendicular to the x-axis forms a circular disk of radius r = 1/x, each with an area of π*r² = π*(1/x²).

The total volume is the sum of an infinite number of these disc areas with thickness dx. As an integral,

V = π ∫₁^∞ (1/x²) dx.

This is a simple integral that converges to a value of 1. We could use the power or rule or our favourite computing software (I used Maple below).

Hence, V = π ∫₁^∞ 1/x² dx = π*1 = π. This means the horn contains only π cubic units of space, even though it extends infinitely far.

Now let’s compute the surface area of the horn. For a surface of revolution, the surface area is

A = 2π ∫₁^∞ y √(1 + (y′)²) dx.

Since y = 1/x, we have y′ = −1/x². Substituting into the formula gives

A = 2π ∫₁^∞ (1/x) √(1 + 1/x⁴) dx.

Software like Maple can easily handle this integral. It tells us the integral diverges to infinity.

However, this is difficult to solve analytically. To understand what happens to this integral, notice that for large x, the square root term is very close to 1, since 1/x⁴ can be approximated as 0 as x grows large. This means the integrand behaves roughly like 1/x (it's actually slightly larger than 1/x). But

∫₁^∞ 1/x dx diverges, and ∫₁^∞ (1/x) √(1 + 1/x⁴) dx > ∫₁^∞ 1/x dx, so ∫₁^∞ (1/x) √(1 + 1/x⁴) dx must also diverge. As a result, the surface area of Gabriel’s Horn is infinite.

This leads to the famous, surprising conclusion:

The horn has finite volume.
The horn has infinite surface area.

In other words, it could be filled with a finite amount of paint, but it would require an infinite amount of paint to coat its inside surface.

Of course, real paint has thickness, so the paradox disappears in the physical world. Eventually, the horn would become thinner than the paint layer itself. But mathematically, the result is perfectly consistent.

The key idea lies in how quickly the function 1/x shrinks. The cross-sectional area of the disks scales like (1/x)² = 1/x², and the integral of 1/x² converges.

But the circumference of each slice scales like 1/x, and the integral of 1/x diverges.

So as the horn extends outward, the added volume decreases quickly enough to sum to a finite value, while the added surface area decreases too slowly and accumulates forever.

Gabriel’s Horn beautifully illustrates one of the central themes of calculus: infinite processes can produce results that feel deeply counterintuitive.

Volume and surface area seem closely related, but can behave in completely different ways when infinite limits are involved. A shape can stretch endlessly yet still contain a finite amount of space.

This strange object reminds me that mathematics isn’t just about calculating numbers, but is also about exploring the strange and fascinating consequences of simple ideas pushed to their limits.