Recurrence Relations! The Fibonacci lecture just became more interesting: V4.8 gives you sequences and a simple set of operators that use them. So yes, Fibonacci away, or create your own sequence definitions, then watch them play out on the screen. Be sure to read about it on the New Features page. Also, there are seven other noteworthy features or enhancements that make DragginMath easier to use, including easier ways to set, get, and use the values of variables. We even improved its detection of your flick gestures.

Version 4.7 is pretty busy! You can now position traditional notation by dragging it around. Logarithms do more in several ways, including replication. Be sure to read the New Features page about that. If you were never quite sure what a logarithm is, now you can see it clearly. Redo animations are easier to follow. The main info page has links to our YouTube channel. Problem History Tracking is easier to use and more useful, especially for teachers. And mode colors on the screen are easier on the eyes.

Version 4.6 offers more ways to factor integers. Double-tap a number to see the Factorization Dialog. Choose fully expanded prime factors e.g. 2*2*2*3*3*5, or prime factors with their exponents e.g. 2^3*3^2*5, or build the specific factors you need from an interactive list. These choices are especially useful if you're teaching or learning fractional arithmetic.

Version 4.5 fixes a problem introduced by iOS v18.4.1. Be sure to upgrade to DragginMath v4.5 as soon as possible. This version also improves the rendering of roots and powers in traditional notation. And now you have a choice in how the prime factors of integers are delivered when an integer is double-tapped.

Multinomial Expansion! Algebra classes usually spend some time on binomial expansion: (a+b)↑n. DragginMath has always been able to do this for specific n by double-tapping ↑, but then you must manually collect like terms. Now DragginMath can do this for you, not just for binomials, but for general multinomials: (a+b+c...)↑n. Just drag the topmost + up onto ↑.

Minor changes: The Solve Part/Full switch is now Clean Solve Off/On. Negative Infinity is now a distinct value. You can turn Magenta Mode off. DragginMath is no longer available on the Mac due to subtle compatibility issues.

The Associative and Commutative Properties are the foundation of algebra, but they are not the most convenient tools for rearranging terms in an equation. And yet the way people usually do it in practice is rarely explicitly taught: most figure it out on their own without fully realizing what they have done. It may not even have a standard name. We call it the Permutative Process. Version 4.2 introduces this important symbolic technique into DragginMath.

DragginMath has always been able to do fractional arithmetic automatically. Now you can do it manually, step by step. Distribute denominators or denominator factors by dragging them to nearby additive operators, then factor to see all numerators over one denominator. Give great demos by showing this with Traditional Text.

Flip a configuration switch to see traditional math notation along with DragginMath's operator trees. This is yet another point of connection in your algebra journey. Now you can directly compare what you're doing in DragginMath to what you see in your textbook.

The introductory ℹ pages "Why Use This App?" and "How To Use This App" have been completely rewritten. These will get you started. Read these either in the app or on the www.brising.com website under "DragginMath Help". For a comprehensive manual, read "The Guided Tour" on the website. From now on, whenever you receive a new version of DragginMath from the App Store, a notifier encourages you to read the New Features page. This only happens once per version update. While you are entering an expression in a text field, that text is now right-aligned. This lets you see what you are typing when your expression becomes longer than the text field, which happens often on iPhone. When you end the line, the text reverts to the familiar left-alignment. Flicking left on a node now offers more choices. Yes, you can still delete a tree if you flick left on its root. You can also copy any node as a separate tree. Or you can copy a node as text so you can paste it into another app.

Flick right on any node to perform Balanced Injection. For equations, this becomes the familiar "Do The Same Thing to Both Sides", but it works for other kinds of expressions, too, and you can use it to solve a wider range of problems. Read about Balanced Injection on the main info page, or look for the info icon on the dialog when you flick right on a node. This new feature was redesigned and renamed after a less useful attempt that appeared only in Version 3.3. If you have defined a Named Expression using the ≕ operator, you can access that value when you double-tap on a similarly named variable node. Look for nodes with wider borders to identify those whose values you have defined. Factorizations are more responsive to the context in which they occur: the side you drag determines the side of the result. For example, factoring the first a out of ab+ca gives a(b+c), but factoring the second a gives (b+c)a.

Screen layout problems on iPhones are now fixed.

See interesting new expansions of the Permute and Combine operators. More helpful interactions between sign and raise operators. More powerful Named Expressions.

Version 3.5 introduces the Antifactorial ¡ operator so you can solve equations involving factorials. Also, try the new Permute ⓟ and Combine ⓒ operators.

Some algebra problems need you to reverse a subtraction or invert a division to make the next step work easily. Flick down on these operators to make this happen in an algebraically safe manner. That pesky dash character (-) means three different things in traditional math notation, and different people have different ideas about how they should be handled. DragginMath now gives you options, so you can explore these issues.

Doing arithmetic is simpler in this release: just double-tap the root node of a subexpression to evaluate. The old way of doing it (drag down into Green Mode) provided a feature no one uses. Green Mode still works for now, but will be delete from a future version. Sometimes you need to invent a term inside an equation. For example, you might need to add 1 to make something work. Of course, this means you must subtract 1 someplace else to keep everything in balance. So flick right where you need this new term to appear, then enter what you need to invent and click the new relationship. Give it a try!

DragginMath's input notation for logarithms has been improved, along with some bug fixes.

Solving equations in DragginMath has always been easy: drag operands up onto the equal sign. For example, to solve x+3=y for x, drag 3 up onto = to see x=y-3. But some teachers think this is too helpful. At the very beginning of algebra instruction, it might be better to show x+3-3=y-3, then leave the user to clean up the +3-3. Version 3.1 has a new Solve switch. Choose Solve Full for the classic DragginMath behavior that cleans up for you, doing more with less work. Or chose Solve Part to see and understand all the details when you're just getting started. Sometimes you discover your current expression needs to be included within some larger expression. So tap the top text to start a new expression, then enter empty parentheses ( ) to insert a copy of the previous expression into the new expression. No more retyping! Transform equations using a new feature that looks suspiciously like the Distributive Property, but for operators over relations. For example, if you have the equation y=mx+b and you need to multiply both sides by 3, then add 1 to both sides, enter 3*(y=mx+b)+1. Now drag = up onto +. See the result 3y+1=3(mx+b)+1. Works for all operators over all relations, not just =. New layout parameters allow you to work on problems almost twice as large.

DragginMath 3.0 is mostly about an improved user interface. It looks a little different: our homegrown math font was replaced with a standard math font. The app's behavior is not affected by this visual change. Touching any part of an algebraic picture highlights the corresponding symbols in the algebraic text. Any part of the algebraic picture can now be compressed into a traditional line of symbols by flicking up on it. Then flick down to convert it back into picture. Left-handed users finally get some respect: choose a left-handed screen layout if you prefer that. DragginMath has always had different screen layouts for iPad and iPhone. iPad Mini now uses the iPhone layout. And, of course, improvements to the algebra.

DragginMath 3.0 is mostly about an improved user interface. It looks a little different: our homegrown math font was replaced with a standard math font. The app's behavior is not affected by this visual change. Touching any part of an algebraic operator tree highlights the corresponding symbols in the algebraic text. Any part of an operator tree can now be compressed into a traditional line of symbols by flicking up on it. Then flick down to convert it back into an operator tree. Left-handed users finally get some respect: choose a deliberately left-handed screen layout if you prefer that. DragginMath has always had different screen layouts for iPad and iPhone. iPad Mini now uses the iPhone layout. And, of course, improvements to the algebra.

Better visualization of expression parsing. More logarithmic transformations.

Double-tap numbers to factor into primes. Improved algebraic replication. A factorial operator!

The Distributive Property and its relatives are now more powerful and easier to use. You can still do the specific distributions found in earlier versions, or you can do general distributions based on what the app finds throughout the operator tree. Also, you won't notice some bug fixes because those bugs are no longer there!

V2.1 has more ways to use unary operators: drag them up and down the operator tree to the most useful place, but only ever to a correct place. Also, usability improvements for annotations.

V2.0 does more and better algebra. Absolute Value using the ‖ operator. More useful behavior for ±. Improvements to existing algebraic behavior. Animated Redo - V1.0 redo only showed the results of changes to your equations. V2.0 Animated Redo shows you which operator or operand initiated a change, which operator was the target of the change, and then animates the change just as if your finger was doing the work. Annotated Demonstrations - Teachers or curriculum developers can optionally add annotations before and/or after each problem step. These are remembered in DragginMath files along with the algebra. Together with Animated Redo, this makes DragginMath an even better tool for remote instruction. Email Conversations - Teachers can send DragginMath file attachments to their students, who watch Annotated Demonstrations using Animated Redo, then work on problem sets. When complete, DragginMath makes it easy for students to email their work back to the teacher. Emails are conveniently titled to help teachers with assignment management. This is seamlessly integrated with the iOS Mail app.