Can Pi be trademarked?

pi logo


Intellectual property law is complex and varies from jurisdiction to jurisdiction, but, roughly speaking, creative works can be copyrighted, while inventions and processes can be patented. In each case the intention is to protect the value of the owner’s work or possession.

For the most part mathematics is excluded by the Berne convention of the World Intellectual Property Organization WIPO. An unusual exception was the successful patenting of Gray codes in 1953. More usual was the carefully timed Pi Day 2012 dismissal by a US judge of a copyright infringement suit regarding Pi, since “Pi is a non-copyrightable fact.”

Pi period

In January 2014, the U.S. Patent and Trademark Office granted Brooklyn artist Paul Ingrisano a trademark on his design consisting of the Greek letter Pi, followed by a period. It should be noted here that there is nothing stylistic or in any way particular in Ingrisano’s trademark — it is simply a standard Greek Pi letter, followed by a period. That’s it — Pi period. No one doubts the enormous value of Apple’s partly-eaten apple or the MacDonald’s arch. But Pi.?

We live in an era of aggressive patent trolling by vulture patent firms. There is vast amount at stake. Think of the current smartphone patent wars and the sometimes successful patenting of life forms. Additionally, it is often cheaper for a firm to pay than go to court. A vague patent can be a “nice little earner,” and thus even established firms such as Microsoft and Apple go patent trolling. Other firms are more willing to “open source” some of their intellectual property, such as, for example, Tesla’s announcement that it will open some of its patents to help spur the electric automobile industry.

What happened next ?

To underscore that he means business, Ingrisano, through his lawyer Ronald Millet, sent a letter to, a Pi novelty company, to: “Immediately cease and desist” their “unlawful” usage of their Pi trademark or “any confusingly similar trademark,” and, within 14 days,

  1. Provide an accounting of all sales of any products containing their trademark.
  2. Provide an inventory of all relevant products.
  3. Disclose any other uses, electronic or print, that have been made of the trademark.
  4. Provide an account of the date when the Pi trademark was first incorporated into their products, a list of all known links to Zazzle’s webpage, and a list of third parties who offer such products.

The letter threatened attorney’s fees and “treble money damages.” The full text of the letter is available here.

Implied in the letter is the plaintiff’s position that “any confusingly similar trademark” includes the Pi symbol itself, without the period, since none of the products offered by Zazzle features a Pi followed by a period. Indeed, according to a report in Wired, Ingrisano’s attorney Millet has asserted that many items for sale by Zazzle “clearly have a pi sign and look similar enough that folks out there might confuse it with products that my client also sells.”

Zazzle responded by temporarily banning all garments featuring the Pi symbol, which involved “thousands of products,” according to the Wired report. But two days later, after being flooded with complaints, Zazzle restored the products. Millet is consulting with Ingrisano as to their next step.

Along this line, it is amusing to note that a Pi design is featured by the Mathematical Association of America as a finalist for its 2014 T-Shirt Contest (and the design includes one formula that one of the present authors was instrumental in discovering). Will MAA be challenged as well?

The smiley face

This spat is reminiscent of a dispute over the “smiley face” between litigants Wal-Mart Stores and SmileyWorld, a London-based company that registered rights to the smiley face many years ago on behalf of Franklin Loufrani. The dispute was finally settled in June 2011, under undisclosed (but likely quite expensive) terms.

Unlike the Pi case, no one has argued that the smiley face has scientific significance! But the case does demonstrate that such disputes must be taken seriously. Moreover, the smiley face is a defined and recognisable image and Loufrani explicitly makes no attempt to stop the use of it in email as plain text, such as :).

Pi in modern mathematics and science

The Pi. trademark, and the aggressive actions taken by the trademark holder, may seem amusing, and are certainly unfortunate for Zazzle and its owners, employees and customers.

But much more is at stake here. If Ingrisano and his attorney prevail in their legal actions, this would mean, in effect, that anyone who uses the Pi symbol in any context would live under the threat that they might receive a similar “cease and desist” letter, with the threats of significant financial loss. This would be an unmitigated disaster for modern mathematics and science.

It is not the slightest bit an exaggeration to say that Pi is the most important irrational constant of modern mathematics. Each year, the Pi symbol appears in thousand of published books and in tens (possibly hundreds) of thousands of technical papers, not just in books and papers related to geometry but also in fields as diverse as statistics and quantum physics.

In fact, the numerical value of Pi (expressed in binary digits) is contained in every smart phone ever produced, since the computations performed to process wireless signals (using the “fast Fourier transform”) inherently involve Pi.

Pi appears in several guises in the equations of quantum physics, and thus is central to semiconductor electronics. Pi even arises in GPS technology, since the frequency of clock signals broadcast by GPS satellites must be adjusted according to the formulas of Einstein’s general relativity, the equations of which involve Pi.

The mind reels at the thought that the authors of every mathematical, scientific or engineering paper that uses a Pi symbol must live under a cloud of worry that they too might be accused of “trademark violation” by including Pi symbols in their articles. And can we really not put Pi on our posters and Tee-shirts?

Also, if Pi is placed under a cloud of trademark violation, what is next? The letter e, the base of natural logarithms, which is almost as ubiquitous as Pi? The “sigma” summation sign (another Greek letter)? The integral sign?

What to do

Unlikely? Perhaps. But to even approach such a path, to place even a glimmer of doubt or worry into the workings and communications of modern science would be an unmitigated disaster. No precedent even remotely approaching this scenario must be tolerated by the scientific community. Must the American Mathematical Society or the International Mathematical Union trademark all mathematical symbols — including 5! — as logos and release them under a general public license?

No, the best solution is simply to rescind the Pi. trademark and to block any future attempts at trademarking mathematical symbols. There definitely are precedents for such action, including the June 2014 action by the U.S. Patent and Trademark Office to cancel the Washington Redskins’ registration of their image, which was ruled as disparaging to Native Americans. Surely the needs of the worldwide mathematical and scientific community to use standard notation free from trademark worries is an equally compelling justification.

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