Is Mathway Free? [Answered]

Is Mathway Free?

The short answer is “Yes”

Mathway is free to sign up and it will show you the answer to pretty much any math question!

However, as the picture below shows,  if you want to see the work for the solutions you have to pay a monthly subscription fee.

 

To use Mathway, just type in some math and then the dropdown will provide several options that the app can do for you–all of these options are 100% free ; however, if you want to see how the app got to the solution, then , sorry you have to pay a monthly fee.

 

Screen shot of what you get for free from Mathway

Screen shot of what you get for free from Mathway

Read this article for a more detailed review of the Mathway app. Or you can just try Mathway for yourself and see what you get for free.

Posted in Mathway Tagged with: ,

Which Graphing Calculator to Buy? #backToSchool

Which Graphing Calculator to Buy?

Graphing calculators are vital for secondary math where students may need to check complex problems to be sure they are working them correctly. In fact, some classes, such as calculus, require graphing calculators.

In the Heller Research Associates’ report “Impact of Handheld Graphing Calculator Use on Student Achievement in Algebra 1”, the research firm surveyed Algebra I teachers from two separate school districts. The survey showed that the teachers wound up using the calculators about 61.9% of the time for instructional activities. The teacher’s felt that the use of calculators “allows them to take the concepts to a higher level and connect the different concepts”.

The National Assessment of Educational Progress (NAEP) found that students in grades 8 to 12 had a higher NAEP score when they used graphing calculators. For high school and college math and science, a graphing calculator can mean the difference between a passing and failing grade. But, with so many different models on the market, it can be difficult to decide which one best.

A graphing calculator is a handheld calculator that completes tasks involving variables, solves equations and plots graphs. Most of the popular models recommended by educators and college testing companies are also programmable. This means that the calculator can be programmed so that complex series of calculations that are frequently used can be automated. Users can also automate calculations that aren’t easily accessible from the calculator’s keyboard.

Texas Instruments

Although free online versions of TI calculators, like our site, become more popular each year, the fact is–the vast majority of high school students will not be able to access these free or web based tools during class time, so, let’s look at what calculator you should buy for school!  This question inevitably leads, at least here in the US,  to  Texas Instruments.  (TI) dominates the marketplace. While there are other brands out there, TI is probably the most recognizable. According to the Washington Post, TI released their first graphing calculator in 2004 and sells that same model to this day, along with several other calculator models from which to choose. According to NPD Group, out of the approximately 1.6 million graphing calculators sold in the U.S. last year, 93% were TI calculators. Casio made up the other 7% of sales.

SAT/ACT Friendly Models

The ideal graphing calculator is one that will take your child from Algebra to Chemistry and on into standardized college readiness tests, such as the SAT and ACT. According to the ACT website, prohibited calculators are those “with built-in or downloaded computer algebra system functionality”. Some models the site lists as prohibited include the TI-89, TI-92 and TI-Nspire CAS. The models below are all test friendly and thus can be used in high school and college classes and also during the SAT and ACT. The top models are all Texas Instruments with Casio coming in sixth.

TI-83 Plus

As of September, 2014, the TI-83 Plus was the number three best-selling graphing calculator on Amazon. The calculator is recommended for:

  • Pre-Algebra
  • Algebra 1 and 2
  • Trigonometry
  • Statistics
  • Business & Finance
  • Calculus
  • Biology
  • Chemistry
  • Physics

Although this is a more basic model than the 84 and above, it offers some strong features.

  • Ability to display graphs, equations and coordinates at the same time on a split screen. This means the student can trace a graph while looking through table values
  • Clear 64 X 96 pixel resolution LCD screen
  • Storage and analysis for up to 10 functions

Best For: Students taking core math but do not have a strong focus in math or the sciences
Suggested Retail: $149.99

 

TI-84 Plus

TI-84 Plus is currently the number one selling graphic calculator on Amazon with a 4.5 out of 5 star review rating. The calculator is recommended for:

  • Pre-Algebra
  • Algebra 1 and 2
  • Trigonometry
  • Geometry
  • Precalculus
  • Statistics
  • Business & Finance
  • Calculus
  • College Math
  • Biology
  • Chemistry
  • Physics

The 84 does everything the 83 does, but has some added features.

  • Comes with 12 preloaded apps
  • Faster processor (2.5 times faster)
  • More memory than the TI-83, with 24 KB RAM and 480 KB of Flash ROM
  • USB cable for sharing files with other calculators or connecting to a PC

Best For: Students taking core math but do not have a strong focus in math or the sciences. However, this calculator also is recommended for Geometry.
Suggested Retail: $189.00

TI-84 Plus C Silver Edition

The TI-84 Plus C Silver Edition graphing calculator is the number two top selling graphing calculator and is recommended for:

  • Pre-Algebra
  • Algebra 1 and 2
  • Trigonometry
  • Geometry
  • Precalculus
  • Statistics
  • Business & Finance
  • Calculus
  • College Math
  • Linear Algebra
  • Biology
  • Chemistry
  • Physics

The entire line of TI-83 and TI-84 Plus models are all in the same family and have all the basic functions of the younger generation. In the TI-84 Plus C Silver edition, the calculate also has features such as:

  • Color LCD display
  • QuickPlot
  • Fit Equation
  • Ability to download images
  • Slide-on case

Best For: Good for students taking all the courses mentioned for the previously mentioned TI models, plus calculus. 1000 SAT prep questions are preloaded on this calculator, so perfect for SAT prep.
Suggested Retail: $150.00

 

TI-Nspire CX

If you have a bit more to spend or you want a calculator that will take you through pre-algebra to college math, the TI-Nspire CX is suited for:

  • Pre-Algebra
  • Algebra 1 and 2
  • Trigonometry
  • Geometry
  • Precalculus
  • Statistics
  • Business & Finance
  • Calculus
  • College Math
  • Differential Equations
  • Linear Algebra
  • Life Science
  • Earth Science
  • Physical Science
  • Biology
  • Chemistry
  • Physics

Some of the unique features of the TI-Nspire CX include:

  • Transfer class assignments from calculator over to a computer
  • Ability to color code equations, lines and points
  • Color display
  • Backlight
  • Lightest weight of the TI models
  • 3D graphing

Best For: College bound students and those focusing on math and science. Also good for SAT prep.
Suggested Retail: $165.00

A good graphing calculator is an investment, but choose wisely and it will last through four years of high school and beyond. While new models arrive on the market from time-to-time, the basic functions of the calculators remain the same, meaning you can also pass this tool down from one child to the next without having to reinvest in a new calculator every few years.

 

 

Posted in Hand Held, TI Calculators Tagged with: , ,

Do Scientific Calculators Make us Lazy

Do Math and Scientific Calculators Make Us Lazy?

Ever since they came on the market about 50 years ago, handheld math, calculus, and scientific calculators have fueled a debate that still rages on to this day. Do they strengthen our fundamental math and science skills and fuel our intelligence? Or do they just make us mentally lazy and perpetuate a counterproductive effect, causing academic weakness?

Calculating the Value of Handheld Calculators

At the core of the divisive issue is whether or not today’s students still learn to think mathematically and scientifically and to apply math theory as their predecessors were forced to do in the days before calculators. Naturally, in the digital age, we tend to think of this as an exclusively contemporary phenomenon or controversy applicable only to the 21st century. But great thinkers have actually been grappling with the issue of labor-saving technology and its impact on students for centuries.

The ancient philosopher Plato, for instance, worried that the technology of writing would dumb-down the population. Yes, as hard as it may be to believe, back in those days writing down words – the invention of basic penmanship – was considered “new high tech.” Plato assumed that once people gained ease of access to written information they would no longer put in the effort to develop an individual capacity for critical thinking. They would lose their scientific curiosity and their academic vigor would diminish.

Doing it the Old Fashioned Way

Plato’s fears were unfounded, and writing has the opposite effect, opening up a whole new world of information exchange. Similarly, it would be foolish to assume that if we would ban handheld computers we would have more innovation in the scientific world. But that should not take anything away from argument that students should still learn the fundamentals, either.

Nobody is arguing that the rigor and know-how it takes to operate a slide rule or perform complex calculus by hand on a blackboard is not a great asset. We should celebrate anyone who has those skills, and we should not stop teaching them just because we now have digital devices and circuit boards. Slide rules can definitely get the job done, even if it does takes weeks to solve a problem that a Texas Instruments device can solve in a matter of seconds. We have Stonehenge, the Egyptian pyramids, jet engines, nuclear weapons, and computers to hammer that point home. Aeronautic engineers did, after all, put a man on the moon using the simple slide rule.

Scientific Calculators Fuel Scientific Discover

If we want to be really ironic we can point to the fact that the scientific calculator made by Texas Instruments is one of the most useful and innovative creations in the history of modern math – but even it was invented without the help of a scientific calculator. But there is no question that without handheld graphing and scientific calculators many scientific discoveries and technological innovations would not be possible.

What is perhaps most important to consider is that the people who gave us those innovations may not have pursued math and science in the first place, without the convenience of the calculator. As students they may have struggled too much with the painstaking pencil and paper methods, and given up or changed their academic focus and career goals. But if the act of learning math is drudgery, they will be discouraged.

Removing Barriers to Education

That claim is supported by a study done at Arizona State University which revealed that students at all levels of learning do, indeed, benefit from using calculators. Educators quoted in the study found that the confidence of students increases, and so does their ability to engage in problem-solving. The research also indicated that the graphing calculator helps students develop more abstract algebraic thinking.

Perhaps the most compelling contribution from that particular research at Arizona State was the revelation that having access to calculators allows many students to overcome barriers to computation. The gadgets give them a significantly enhanced opportunity to learn, explore, and advance in mathematical and scientific academics.

Teach the Basics but Utilize Technology

The bottom line is that technologies like the scientific calculator give us a tremendous advantage. To make the most of them and leverage their value to the optimum, however, we also need to continue to teach students the basics of math and science. The two go together, which is why “pencil and paper” math has a place in today’s classroom alongside the modern calculator.

Giving students the knowledge to use both will empower them with a better, more well-rounded grasp of underlying theory and its practical applications in the real world. Then, armed with that kind of rich basis of knowledge they will be able to do exponentially more with the modern tools of the trade such as the scientific graphing calculator. Make it easier to solve problems by giving students the right tools and they will be inspired to solve more of those problems. Since solving problems is the goal of math and science, the handheld calculator is priceless.

Related links:

http://www.calvin.edu/weblogs/deusexmachina/do-calculators-and-gps-make-us-stupid/

http://news.discovery.com/tech/technology-brain-intelligence-20130319.htm

http://books.google.com/books?id=ntGpV3rMjnoC&pg=PA49&lpg=PA49#v=onepage&q&f=false

Posted in TI Calculators Tagged with: , , ,

What was used before Calculators?

Before Calculators, what was used?

Humans have been counting, calculating, and charting since the beginning of time. At first they used their fingers and then such things as piles of pebbles, bundles of twigs, and simple mechanical devices like the revolutionary abacus. It is hard to imagine a time when we all didn’t have a calculator in our school bag or online, but for the majority of human history, that was the case. So, let’s have a look at how humans got by, for so long, without a calculator.

Picture of an abacus

Picture of an abacus

The Abacus and Counting Board

The abacus is a simple frame comprised of rods on which beads are moved to represent various groups of numbers. For centuries the abacus was a cutting edge device used by the Chinese, Greeks, and Romans. There is also evidence that the Aztecs in present-day Mexico and Central America used a type of abacus made from kernels of corn strung on pieces of thread.

The word abacus, from Latin, means “tablet,” so in one sense the abacus was the earliest version of the tablet computer. Next came the counting board, which was usually made from a slab of wood or stone with lines carved into it. Beads were slid from one position to another across the board to aid in counting and carrying numbers over to higher values.

The Advent of Arabic Numbers

Calculations can, however, be performed much faster using Arabic numbers compared to Roman numerals or beads on an abacus. As the use of Arabic numerals spread in popularity across Europe and the abacus and counting board became rather obsolete.  The implementation of the Arabic system in Western Europe is credited to Leonardo of Pisa – who lived where the famous tower of Pisa is located.

Also known by the name Fibonacci, he was a mathematician of the early 13th century who wrote a groundbreaking book about numerical calculation called “Liber Abaci”. The book was based upon the Arabic numbering system that his father, a merchant seaman, had learned while traveling to various Middle Eastern cities along Mediterranean Sea.

The Use of Tables

Since shortcuts make it faster and easier to perform calculations, tables are a great resource. Instead of slowly adding up lots of small numbers, for example, we can simply refer to our multiplication tables and do complex arithmetic in our heads. Similarly, as calculations of such things as geometry, algebra, and calculus were done over the years people created tables to use as shortcuts. Those were, in turn, compiled into handy reference charts or books.

One of the classic examples is a book titled “CRC Standard Mathematical Tables and Formulae,” which has been around for about 40 years. In the days before calculators, students and engineers would refer to this large book to find formulas, tables, diagrams, integrals, and other data that helped them as they performed calculations by hand. With more than 6,000 entries, and such things as trigonometry tables accurate to the nearest minute, this kind of book was invaluable in the days when calculations had to be done by hand.

The Mechanical Slide Rule

John Napier of Scotland, who lived in the 1600s, invented logarithms – another kind of shortcut. He also constructed the first slide rule to make it easier to use with those logarithms, and his slide rule was a paradigm-shifting innovation.

The slide rule became very popular across Europe and was in widespread use by the 1800s. Amédée Mannheim invented one of the first modern slide rules in 1859, and used it to calculate how to fire artillery to hit a target accurately when he was in the French army.

Modern Slide Rules

Modern slide rules, like those used throughout much of the 20th century, are about two feet long and two inches wide and have three basic components. The main part of a slide rule resembles a ruler and is marked with scales. Then there is a sliding section that moves along that ruler-style part. The third component is a curser or pointer to set specific points along the scales.

These devices were used by students, architects, scientists, engineers, and others who would perform their calculations by using their slide rule while referring to charts and tables. Then they would finish their calculations or draw their graphs using pencil and paper. Yet, as I am sure you can imagine,  even this advancement is still far away from the convenience and efficiency of a calculator.

Progressing into the Digital Age

Naturally, this process was time consuming and labor intensive. The accuracy of slide rule calculations is subject to human error, too, because if you accidentally read the tiny marks on the scale incorrectly or place the cursor in the wrong place the results will be flawed.  Now, while you can argue that a calculator is also prone to this type of human error, but, the odds of incorrectly pressing a key on your calculator’s keypad is obviously less than the chance of someone making an error in this process;  Oftentimes a group of five or six students working together as a team might need an entire class session to solve a problem.

Today, thanks to automated digital calculators, a student acting alone may solve those same problems with reliably accurate results within a matter of minutes, if not seconds. They can use a basic handheld graphing or scientific calculator or the kind of fast, intuitive, free calculator that is available here at www.meta-calculator.com .

References:

http://en.wikipedia.org/wiki/Hardware_multiplier

http://en.wikipedia.org/wiki/Linear_interpolation

http://web.mit.edu/2.972/www/reports/slide_rule/slide_rule.html

http://www.ee.ryerson.ca/~elf/abacus/history.html

Images

http://en.wikipedia.org/wiki/Abacus#mediaviewer/File:Boulier1.JPG

Posted in History Tagged with: ,

Are TI Graphing Calculators Obsolete?

Are TI Graphing Calculators Obsolete?

Texas Instruments (TI) graphing calculators are virtually unchanged over the years, leading many industry observers to wonder if they are now obsolete. Judging from their enduring popularity, however, it seems that these reliable dinosaurs are here to stay, at least for the foreseeable future.

A Throwback to the Pre-Digital Era

The TI graphing calculator is reminiscent of the pre-digital era when it was first introduced. Compared to today’s small, sleek, fast, multipurpose electronic devices it has limited speed, functionality, and versatility. All of the TI graphing calculator models also feature mundane design aesthetics highlighted by bulging buttons, small screens, and thick industrial-style housing.

They lack the visual and technological attributes of today’s gadgetry and essentially look like something a student’s father or grandfather would have used. But the truth of the matter is that the parents and grandparents of today’s youngsters probably did use a TI graphing calculator that is nearly identical to those marketed and sold now. Meanwhile they still have a rather steep price tag when compared to the electronic devices of today.

A Highly Profitable Product

Despite being a vivid example of outdated and potentially obsolete technology, the graphing calculator still contributes dependable profits to TI. Research published in the Wall Street Journal indicates, in fact, that TI controls approximately 80% of the USA market for graphing calculators. The company’s own annual report relegates sales of the gadgets to a miscellaneous category that includes other types of calculators and electronics. But that segment generated $2.6 billion in 2013, which was 21 percent of the company’s total revenues.

Back in 2007, when TI calculator sales were still separated as a distinct line item in SEC filings, they contributed $526 million in revenues and $208 million in profits. That represented about 5% of TI’s total annual profits. Based on that history it is logical to assume that graphing calculators are still a viable “cash cow” product for TI.

Enduring Popularity

Another reason that the TI graphing calculator has remained popular is that students are still permitted to use models like the TI-84 when taking college board exams. More advanced and capable models  that fall into the category of computer devices are not permitted, and neither are WiFi-enabled gadgets like smart phones.

In most cases, therefore, the most powerful and function-rich device that a student can take into the exam room is a reliable but old-fashioned TI graphing calculator. That is a compelling reason to invest in one. A much more sophisticated calculator is of little use to a student if it is banned. Faced with a practical choice, in other words, students continue to prefer the TI because it is more relevant to their day-to-day educational experience.

Institutionalized Popularity of the TI Calculator

Casio offers entry level graphing calculators that sell for around $50, but Casio has nowhere near the market share and graphing calculator brand recognition enjoyed by TI, at least here in the US. Teachers are also reluctant to recommend that students buy anything but a TI calculator, because it is more efficient to instruct students who are all using the same basic platform to do their calculations.

If there are multiple types of devices in use, instructors must learn the unique operations of each of those gadgets. They may also need to edit and revise their handouts and class materials to accommodate different ways of performing calculations on devices that operate somewhat differently from one another. Additionally, for the student him or herself, it is much more convenient to simply use the type of calculator that the teacher recommends and will use in lessons.

But the TI models remain perfectly suited for the high school classroom, year after year. Until educators are ready to radically change their teaching methods, textbooks, academic handouts, and exam protocols the TI graphing calculator will remain the one that the majority of teachers recommend or require.

Relevance Rules

Recently competitors of TI also began designing relatively inexpensive smart phone apps. Hewlett-Packard (HP) offers a graphing calculator app, for example, that sells for about $30. Still, HP cannot seem to penetrate the market for the TI calculator because once again, students prefer a device that is relevant to their situation.

For students who are not yet at the collegiate level, $30 can be a lot of cash. Even students who have that kind money to spend probably have other shopping priorities. For the price of a graphing calculator app they could download 30 or more songs from the iTunes store – a more likely choice for a teenager. Plus there are many students who may not have cell phones, or who have economy-priced models that do not run smart phone apps. Perhaps more importantly, smart phone use is prohibited in most classrooms, which eliminates the possibility of using smart phone apps during class.

Parents who are already straining the household budget to pay for their child’s extracurricular activities may also have a tough time justifying an additional $30 expense to buy a single app that cannot be used in class or to take standardized tests. That is especially true if they already had to shell out $100 or so to buy a handheld TI graphing calculator. Of course the good news is that if a mom or dad used the same TI calculator when they were in college, they can just hand it down to their kids since it has not gone out of style.

A Fee-Free Alternative

Of course, there is also a new class of graphing calculators that have evolved–free online ones like the one on this site! We hope that our tool offers a free, user-friendly online graphing calculator for virtually all grade levels.

The tool gives instant, accurate answers and allows the user to perform a variety of functions that are just like those done on a handheld TI graphing calculator. Graph any equation, find its intersections, and create a table of values. The site also offers other calculators including those for science and statistics, as well as a handy programmer’s calculator.

In the end though, despite all of the technological advances of the last two decades, the TI graphing calculator has defied the odds by remaining very relevant and useful, even as other technologies have outpaced it in both functionality and affordability.  Until something changes in the world of education and testing, there  is little chance that the classic hand held graphing calculator is going to change.

References:

http://www.ti.com/corp/docs/investor/fininfo/other.shtml

http://192.168.1.1:8181/http://files.shareholder.com/downloads/TXN/3320765500x0x730843/54d68a12-74d7-4dad-83da-5e2c22a97b5e/TI_2013AR_2014PS_Web.pdf

http://online.wsj.com/news/articles/SB125244891686393811

http://www.marketwatch.com/story/numbers-dont-add-up-for-ti-calculator-2009-09-08-191200

http://www.theatlantic.com/technology/archive/2011/08/what-your-old-graphing-calculator-says-about-technology/244028/

http://www.theatlantic.com/technology/archive/2013/08/go-ahead-mess-with-texas-instruments/278899/

http://en.wikipedia.org/wiki/TI-89_series

 

Posted in graphing, Hand Held, Online, TI Calculators Tagged with: , ,

TI Graphing Calculator: Profit Margins

The TI Graphing Calculator: A dominantly stable, profitable product.

In 2009 the Wall Street Journal ran an article which describes that approximately 80% of the graphing calculators sold in the USA were made by Texas Instruments (TI). By contrast, competitor Hewlett-Packard (HP) had less than a 5% stake in the graphing calculator market. The story also reported that overall sales of calculators in 2007 generated $526 million in revenues and $208 million in profits for TI, representing about 5% of TI’s annual profits.

A Small but Profitable Segment

Since 2008 it is harder to ascertain financial data specific to TI calculator sales, because that was the last year that the company reported the results of its calculator sales as a separate and distinct line item in SEC documents and annual reports. Instead they now include those sales under a large miscellaneous category called “Other.” In its latest annual report TI describes this “Other” segment in this way:

“Although there are some differences in the various business models that comprise this segment, in general, most of these products have a profit contribution that is attractive but where our investments are minimal and growth expectations are lower.”

The relatively small category was responsible for $2.6 billion in revenues in 2013, representing 21 percent of total revenue. That is a huge contribution to the bottom line of TI, particularly considering how little the company invests in that segment.

No Need to Innovate

Many wonder, of course, why TI has not kept up with the times and made its graphing calculators more high-tech. The experience that the company had when it introduced its TI-Nspire graphing calculator a few years ago may provide an obvious answer. The product was intended as an improvement over the traditional graphing calculator, with a higher price tag and new features like the ability to create spreadsheets.

But its platform was more like a computer than a traditional handheld calculator, and many consumers complained that it was too complicated and too expensive. Some also said that the Nspire platform restricted user ability to write the kinds of programs they were accustomed to designing and sharing. People who buy graphing calculators expressed their preference for the traditional versions and kept purchasing them, while sales of the Nspire were less than inspiring.

Maintaining the Status Quo

One explanation for this continued consumer loyalty is that the TI-83 and TI-84 models are still an ideal product  for the high school classroom. Teachers prefer to have all students use the same basic kind of calculator because it makes teaching easier, and most standardized tests prohibit the use of more powerful calculators.

There are inexpensive smart phone apps  and free online calculators that perform graphing calculator functions, including one from TI rival Hewlett-Packard. But wireless devices are usually banned during exams and smart phone use is normally prohibited in high school classrooms, which effectively limits practical access to those applications.

For those reasons it seems that TI has little incentive to alter the basic design and functionality of its popular graphing calculator products. At the same time, there is no financial pressure to lower the prices of its unchanged and rather low-tech graphing calculators since consumers are happy to keep buying them.

References:

http://www.ti.com/corp/docs/investor/fininfo/other.shtml

http://192.168.1.1:8181/http://files.shareholder.com/downloads/TXN/3320765500x0x730843/54d68a12-74d7-4dad-83da-5e2c22a97b5e/TI_2013AR_2014PS_Web.pdf

http://online.wsj.com/news/articles/SB125244891686393811

http://www.marketwatch.com/story/numbers-dont-add-up-for-ti-calculator-2009-09-08-191200

http://www.theatlantic.com/technology/archive/2011/08/what-your-old-graphing-calculator-says-about-technology/244028/

http://www.theatlantic.com/technology/archive/2013/08/go-ahead-mess-with-texas-instruments/278899/

 

Posted in graphing, Online, TI Calculators

History of Graphing Calculators

A History of Graphing Calculators

Texas_Instruments_SR-10

Texas Instruments SR 10

It’s easy to forget, when the calculators that are sold in big-box stores across the land, blister-packed in plastic, can perform the most ferociously complex calculations — and display the results in the form of a clear, easily-read graph — that there was a time when even a calculator that could manage more than the four basic arithmetic operations was considered a marvel of modern technology.

While today’s graphing calculators are capable of increasingly sophisticated algebraic processing, the earliest calculators were simple adding machines. Mechanical calculators have been around since 1820 and the Arithmometer, but machines that actually looked like modern calculators didn’t arrive until the middle of the 20th century. 1961 saw the arrival of ANITA (A New Inspiration To Arithmetic), but this was a vacuum-tube-powered monstrosity. The first real calculators — the first machines that might be recognizable as an ancestor to today’s modern graphing calculators — appeared in the 1970s, developed by the British company Sinclair Research and Busicom of Japan, but these were still four-function arithmetic machines. They also sported the green, glowing vacuum fluorescent displays that were typical of the machines of the day.

Texas Instruments made the next major leap, introducing the SR-10, a pocket calculator that used scientific notation and algebraic entry, and its successor, the TI-30 is still, albeit in highly modified form, still on sale today.
But, for all its trigonometric clevernesses, its statistics functions and its dedicated p key — big news when the SR-11 first boasted one back in 1973 — the TI-30 still only displays numbers on its 10+2 display. It’s an LCD display, and it can show up to 12 digits in its answers, but alphanumerics are its only trick.
Over the next decade, calculator innovation was focused on the internal functions of the machine, but the big leap came in 1985, when Casio introduced the fx-7000G, the first commercially-viable graphing calculator. Graphic calculators represent a significant step ahead in two main areas. Firstly, they do more than simply process one calculation at a time — in order to plot a graph, the eventual output without which a graphing calculator would be, well, just a calculator, the device has to perform a whole series of calculations based on an equation or formula or function that the user has input, and then it must store the results of those calculations in its internal memory. This alone requires a considerable increase in processing ability, and also needs a calculator that can handle rather complex inputs, which in turn call for an increasingly powerful display.

Texas Instruments made the next major leap, introducing the SR-10, a pocket calculator that used scientific notation and algebraic entry, and its successor, the TI-30 is still, albeit in highly modified form, still on sale today.
Early calculators, as we’ve seen, presented their answers via vacuum fluorescent displays. These were replaced, briefly, by light-emitting diodes, typically red-digit displays that had the same limitations on size — LEDs are clear and easy to read, but they are better suited to large-pixel displays. The very first liquid-crystal displays, now a mainstay of data-presentation devices from watches to phones to desktop-computer monitors, appeared as early as 1936, but the technology wasn’t truly ready for the kind of high-definition use a graphing calculator requires until the 1980s. Casio’s fx-7000G sported a 96×64 dot matrix, and each dot was either black or white, on or off — there was no grayscale or color in this display.
But what the fx-7000G could do was draw graphs. Thanks to its dot-matrix screen, it could plot, out of the box, algebraic graphs and statistical charts such as bar graphs, normal distribution curves and regression lines. It could also present graphs of user-input functions.

Example Graph of Casio FX 700 G

Graph of Casio FX 700 G

The other key difference between the fx-7000G and many of its predecessors was the fact that it could be programmed. In fact, graphing calculators started to blur the lines between calculators and computers, to the point that the fx-7000G shared much with the Casio BASIC handheld computer, including the ability to store programs in one of ten internal storage slots. The calculator was based on a custom processor designed by NEC of Japan and likely based on the Z80 processor that powered many early home computers, such as Sinclair Research’s famous ZX-80. It had 442 bytes — that’s bytes, not megabytes or even kilobytes — but clever programming saw users shoehorning useful routines like estimating indefinite integrals into minimal storage.

HP 28 Calculator

HP 28 Calculator

Not long after Casio opened up the market for graphing calculators, Hewlett Packard produced the HP-28 series, the first calculators that could solve equations symbolically. With the advent of computer algebra systems such as HP’s, graphing calculators increasingly resembled specialized computers; the ability to draw graphs became an integral part of the graphing calculator’s ability to present ever-more-complex outputs. And with 32 kilobytes — sixty times the storage Casio’s first graphic calculator offered — and a central processor running at 1MHz, the HP-28s, first sold in 1988, had specs that compared favorably with the desktop machines of only a year or two earlier.
HP replaced the HP-28 series with the HP-48, which again closed the gap between handheld and full-sized computing devices. With external data connections via RS232 serial port or a proprietary infrared protocol, the HP-48 also literally narrowed the distance between graphing calculators and desktop computers, providing a data path that enabled handheld devices to send data to a full-sized computer for more complex analysis and processing.

In the two decades that followed, the majority of innovation enjoyed by graphing calculators and their users was focused on processing power. While Texas Instruments’ TI-84, introduced in 2004, still used the same Z80 processor that informed the CPU powering Casio’s fx-7000G, the same processor that Zilog started selling in 1976, it now ran at a dizzying 15MHz. Users increasingly wanted to exploit the full processing power of their calculators, but the small screens and smaller buttons of a typical graphing calculator meant that writing programs on the desktop, compiling them and then transferring them to the calculator via a now-ubiquitous USB cable became the standard means of enhancing the device’s functionality.

Most graphing calculators have their own proprietary programming language, although these languages typically have at least a passing similarity with more established languages. Hewlett-Packard’s graphing calculators are programmed using RPL, which stands for, depending upon who you ask, either ROM-based Procedural Language or, both more accurately and a little more pleasingly, Reverse Polish LISP. Texas Instruments’ calculators prefer to be spoken to in TI-BASIC, but can also be programmed in Z80 assembly language, with C compilers also available.

While the insides of graphing calculators saw considerable progress during the 1990s and 2000s, externally little changed. When the TI-84 appeared in 2004, it boasted 128KB of internal RAM memory, and the ability to access external USB storage, but its interface with the world was still a 96×64-pixel monochrome display — no better than the fx-7000G, nearly twenty years earlier. The TI-84 Plus, in 2004, did, however, allow prettyprinted expressions, as did Casio’s 9860 series the following year. Mathematical expressions could now be displayed in a much more readable way — (x^3+2*y^4)/2 could be shown as CodeCogsEqn
Texas Instruments introduced the NSpire range in 2010, featuring a full-color 320×240 display that enables much more detailed displays of data. The addition of color is particularly noteworthy — more than one color means the ability to display more than one graph. The NSpire range also interacts with Texas Instruments’ Lab Cradle, a development of the Calculator-Based Laboratory concept which was designed to enable a graphing calculator to become a full laboratory computer, able to collect, store and process data from a range of sensors.

With the development of software-only implementations of the graphing-calculator concept, is there still a role for dedicated graphing calculators? The graphing calculator as the hub of a data-gathering system is a niche that smartphone apps are as yet unable to fill — while a phone app is convenient, the phone is a generalist system that lacks the specialist functions that a graphing calculator can offer, such as sensor interfacing or the ability for users to program the calculator. And few schools and national testing organizations are willing to allow students to bring their smartphones into an examination room with them — indeed, increasingly graphing calculators are restricted too, with TI’s NSpire machines featuring a “Press-To-Test” mode which temporarily disables features such as 3D graphs for the duration of an exam.

But while dedicated hardware graphing calculators are increasingly specialized niche devices, math teachers and students are more and more turning to the Web for simple, but ever more powerful, graphing calculators. Meta-Calculator offers all the graphing features of a hand-held calculator, but takes full advantage of your computer’s monitor to display its graphs in full color, making its output clear and easy to read. Hand-held graphing calculators are great for students, but teachers find full-screen graphs invaluable for teaching, and the great advantage offered by web-based applications such as Meta-Calculator is its nimbleness — updating the firmware on a hardware calculator is a dance of downloads, cables and, occasionally, voodoo, but when Meta-Calculator’s developers added a “share” feature to the calculator, or tweaked the software to perfect its cube-root graphs, changes are made on a webserver in a process that’s transparent to the end user, who just sees better and better graphs.

Calculators have changed beyond recognition since the four functions and eight red digits of the pocket calculators of the 1960s and 1970s; today’s software-based graphing calculator apps and websites put what was expensive and highly specialized equipment in the hands of anyone who needs to generate graphs simply and easily.

Posted in graphing, Hand Held, Online, web Tagged with: ,

Share your Graphs- a new feature of the Graphing Calc!

Sharing your favorite graph has never been easier Meta-calculator

We’ve been working hard at meta-calculator to make it easier to share your calculator’s graphs.

Of course, you’ve always been able to download your  graph as an image, but now–if you enter a series of equations into the calculator and want to share a direct link to the actual state of the graph with the equations, you’ll now notice something new at the bottom of the graph screen- a link . This new feature should make it easier for students , teachers or anyone to share their work. At the current moment, only the graphing calculator is shareable; however, we are working on allowing users to share their work for any of the calculators.

Share Graphs directly from calculator

 

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Meta Calculator’s Features

Graphing Calculator

Graphs up to 7 equations

finds intersections

produces table of values

lets you save image of graph to your computer!

, customize, x-scale,y-scale, pan, zoom and more

enhanced trig graphs by setting axes in terms of pi

 

Scientific Calculator

All of the basic functions and buttons you’d expect including sin,cos, sin-1, cosh, log and more.

Plus it has some more advanced features including a button to calculate the least common multiple, permutations, combinations

Possibly most powerful of all—a linear equations solver that lets you input up to 6 equations with either two or three variables and the solver will calculate the solutions.

Memory button for storing calculations for future use

 

Matrix/Vector Calculator

Add, subtract, multiply and transpose matrices

Calculate the determinant or inverse of a matrix

 

Statistics Calculator

The basics like calculating quartiles, mean, median, mode as well as the correlation coefficient

Almost any kind of regression (linear, quadratic, exponential, cubic , Power, Logarithmic, Natural Logarithmic). The regressions and points can then be graphed

 

 

Can Computes student 1 or 2-Tailed T-Tests (paired and unpaired).

 

Overall, this calculator should serve the needs of almost any high school student/college student, but it would also be quite useful for anyone who needs to create graphs for their equations—you can just hop on the internet browse to the web page and download the graph

Posted in graphing, Online

A Reliable Scientific Calculator

Scientific Calculator Reliability

So,  imagine that your Scientific Calculator’s    code  is just one piece of a large app that computes all the different kinds of cool things — ie, imagine it’s Meta Calculator. To your knowledge the code works great, but then, someone emails you about a bug. In this case, someone emailed that typing “—5″ into the Scientific Calc didn’t produce the expected value of “-5″ .

Ok, first off, if you’re wondering who would ever actually type “—5″ into a calculator, you’re asking an understandable , but flawed, question.  The point is not ‘why focus on weird, unrealistic, use-cases’.  But rather that a flaw in scientific calculator’s parser existed. There was a good chance ,  after all, that no one would ever go to our site and type those characters on purpose! In fact, the guy who reported the bug was purposefully looking for bugs  (and it was the only one that he could find).

So, now you’re in the situation of knowing that all of your code works for the countless math expressions but your parser misses one situation. Now, it’s not just the scientific calc that uses the parser–so does our client side graphing calculator ,  the one that we license out to several companies.

Ok, so what do you do? You get that bug fixed!

Darnit–here’s the dilemma:

How do you know that  your bug fix does not introduce new errors in some other part of the calculator? This is called a  regression bug–when you fix one bug, only to introduce a new one somewhere else.

And here’s the solution: Enter unit testing and a battery of  tests that  new algorithms for the scientific or graphing calcs must pass before we push them out to the site. So that every time that you make a change to anything under the hood, you submit the new algorithm to hundreds and hundreds of test calculations to make sure that the app  always arrives at the correct solutions.  In the case of Meta Calculator, currently there are over 1,100 unit tests that we test before pushing out a change to the live site. Let’s look at one unit test– Consider, for instance, the expression  “3 * sin(30)” . We use excel or some other reliable tool to determine an expected resulting value of 1.5 (assuming we’re in degrees). Then we see if the calculator gets the same result (taking, rounding error into consideration of course). This process occurs for each and every unit test. Each unit test involves creating a test expression like 3 * sin(30) and as well as the true answer like 1.5 .

Here are some other screen shots of successful set of tests looks like. As you can see in screen shot below, 1,126 assertions or ‘tests’ passed and there were no errors. When this happens, we know that changes that were made to the calculator did not introduce any other new bugs.

screenshot2

 

 

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