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Origami 101

April 24, 2026

What is Origami?

Origami does not originate from a sole inventor, it was crafted over centuries by many different hands for various ceremonial purposes in Japan and even China (Robinson, 2026). The word we use today, origami, is derived from the Japanese words ori which means folded and kami which translates to paper. While paper itself was first developed in China before spreading to Japan, folding paper into decorative and symbolic forms became especially refined in Japanese culture over time. Early uses of folded paper included religious ceremonies, gift wrapping, and formal exchanges, where presentation held great meaning.

Fast forwarding centuries, today origami is seen worldwide. A simple YouTube search nowadays can teach even the newest of the new how to craft an origami chameleon, like how I learnt! What was once a traditional practice has now grown into a global hobby, mathematical practice, and even an area of scientific research.

 

Math, Science, and Folds

It comes to no surprise when we see the intricate works by masterful artists, that the art within folding comes from mathematical roots. For example, take the common fold that basically all origami pieces start with: the square piece of paper folded diagonally corner to corner and then along the sides, top to bottom and left to right. These folds create lines of symmetry and reference points that help guide more intricate folds later on. Mathematically, these folds create either a valley or mountain based on the value of the angle between the two adjacent planes created by the fold (Kunz, 2024). A valley fold bends inward like a “V,” while a mountain fold rises outward like a mountain. By combining these two simple fold types in different orders, locations, and sizes, folders can create highly detailed animals, flowers, and geometric structures. 

Additionally, origami also has strong roots in more of a geometric application of math, with many models and folds often relying on fractions, bisectors, symmetry and so much more. In the scientific world, origami has received its share of the spotlight from inspiring compact folded solar panel designs for satellite use to shaping medical stents used in patients. 

 

My Folds and Why I do it

My goal when folding is simple: just don’t make it ugly. I find my inspiration, to recreate art through online tutorials, to be fueled by the passion and creativity of others. I folded the blue origami dragon below to surprise one friend, and the raccoon for another. I trace my folding skills back to one main motivation: wanting my creations to be as perfect as possible for the people around me. I have made plenty of lousy folds, but never when I feel a real sense of purpose behind them. When I fold for someone else, I tend to care more, focus more, and try as hard as I can. I am happy to say I will keep carrying on origami traditions. Mine may not be embedded in ceremonial, mathematical or even scientific purposes, but they still come from a place of creativity, curiosity, and humanity.

References

Origami created and photographed by Kristina Siju

Origami with Jo Nakashima. (2021, September 14). ORIGAMI CHAMELEON (Jo Nakashima ). YouTube. https://www.youtube.com/watch?v=if7iSuzNn38

Nakashima, J. (2015). Origami Dragon (Jo Nakashima) [YouTube Video]. In YouTube. https://www.youtube.com/watch?v=kUsxMXwCW8A

Muneji Fuchimoto ORIGAMI CHANNEL. (2020, December 8). 「折り紙」アライグマ（racoon origami）の折り方. YouTube. https://www.youtube.com/watch?v=X2FYuvt-U80

Geometry – Ancient geometry: abstract and applied. (n.d.). Encyclopedia Britannica. https://www.britannica.com/science/geometry/Ancient-geometry-abstract-and-applied

Thesis, B., Kunz, C., & Cannas Da Silva, A. (2024). Mathematics of Origami. https://people.math.ethz.ch/~acannas/Student_Papers/BSc_Theses/2024_bsc_kunz_mathematics_of_origami.pdf

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  Timothy Durham was convicted of rape when a test showed his DNA genotype matched the DNA recovered from the crime scene. Eye witnesses testified that Durham was in a different state at the time of the incident, but he wasn’t exonerated from his 3000 year sentence until follow up DNA analysis showed that the preliminary forensic analysis used in the trial was misinterpreted (Thomas et al.). DNA testing serves an invaluable part in our criminal justice system, but it comes with complications and bias that can lead to wrongful convictions and misinformed juries.  

Background:

Forensic genetics aims to identify the origin of a biological sample. It can be traced back to Karl Landsteiner who discovered human ABO blood groups. With blood groups, suspects could be eliminated based on their blood type. For example, if a suspect had type A blood and there was type B blood left at the scene by the perpetrator, the investigators could rule out the suspect. Unfortunately, the reverse didn’t work. If the suspect and perpetrator both had the same blood type, it can’t be concluded that the suspect was guilty. Blood identifiers evolved into 8 distinct categories which improved the ability to eliminate suspects, but could only conclude that (if the system matched) it might be the perpetrator or this person might be related to the perpetrator (Jobling and Gill). The field evolved in the 1980s with the discovery of Minisatellites, lines of repetitive DNA that don’t encode proteins. Minisatellite patterns in DNA create what we know today as the DNA fingerprint, and it has a much higher accuracy rate than previous methods (Augustyn et al.). Around the same time, a breakthrough for victims of sexual assault was discovered. In the case of assault, bodily fluids of both the victim and the assaulter can get mixed. A process called differential lysis was created which could selectively increase the concentration of sperm in a fluid sample thereby allowing for accurate DNA testing (Jobling and Gill). Forensics evolved to use single-locus probe testing after several years because of its ease of interpretation. It looked at specific minisatellites that had high variability between subjects. This was the first DNA-based method to be used in a criminal investigation. Two murder homicides from several years apart were connected using DNA evidence. The evidence was then used to exonerate an innocent man, and the guilty party was found when he tried to evade mandatory DNA testing for all men in the small town. His guilt was then reinforced when the DNA profiles matched, and he gave a confession (Jobling and Gill). Finding DNA at a crime scene doesn’t guarantee that you’ll find a murderer. There are issues with non-pure samples and limited samples that make DNA work difficult, and accreditation of facilities and new techniques and take time (Jobling and Gill).  

Subjectivity of DNA Interpretation:

In a 2009 publication, the National Academy of Science discusses the possibility for subjective influence in lab based forensics. The interpretation bias happens in complex cases where, for example, there could be a mixture of DNA. A study published in 2011 looked specifically at this issue. A gang rape happened in Georgia, and the mixture in DNA from the case was used to prosecute one suspect after another suspect took a plea bargain to testify against him. With DNA mixtures, there are three possible conclusions: suspect excluded, suspect cannot be excluded, and inconclusive. If the suspect is excluded, it means that there’s little to no possibility that his DNA is part of the sample. If the suspect cannot be excluded, it means that there’s a possibility that his DNA is part of the sample. In the trial, the DNA examiners who knew the context of the case concluded that the suspect being prosecuted could not be excluded. The 2011 study gave the DNA evidence from this case and the DNA profiles of the suspects to 17 forensic examiners. These examiners had no context of the case, and they all worked independently. Of the 17, only 1 came to the same conclusion (suspect cannot be excluded) as the examiners who knew the context of the case. Twelve of the 17 concluded that the suspect who was prosecuted and convicted had no relation to the DNA found in the sample. Not only does this show that subjectivity occurs due to the context of the case, but the 17 examiners came up with different findings based on their past experiences meaning that not all DNA analysis is objective. Some organizations like the Scientific Working Group on DNA Analysis Methods say that quantitative statistical evidence should be presented with every categorical conclusion, but the US doesn’t require this (Dror and Hampikian).

False Positives:

There are two categories that cause wrongful identification in a DNA report: coincidental matches and false positives. Coincidental matches are DNA matches between two unrelated people. The probability of these matches is about 1 to 500,000 for white individuals and about 1 to 350,000 for black individuals. This small probability of coincidental matches makes people feel confident in DNA evidence. False positives, on the other hand, are matches between DNA and test DNA that result from issues in the forensics lab. There have been multiple cases of forensics labs accidentally switching victim and suspected rapist DNA which lead to convictions that were later overturned when the lab realized the error. There are also cases of misreading or misunderstanding a sample. In a case from 1993, a man was convicted of rape because someone interpreted a mixed sample of victim and perpetrator DNA as an individual sample. The conviction was again overturned. To prevent false convictions, retesting DNA is allowed, but it’s not an efficient solution. Many people are pushing for statistical information on the probability of false positives, so that the jurors can make accurate judgements based on DNA evidence (Thomas et al.).  

Conclusion:

DNA analysis is a useful tool for the criminal justice system, but subjectivity can be an issue in forensic testing. To combat wrongful convictions, there are organizations like The Innocence Project who use DNA testing to free the innocent, but reformed forensic testing standards should be put in place to prevent subjectivity and to ensure juries are correctly informed during trials. https://www.innocenceproject.org/    

Citation:

Augustyn , Adam, et al. “DNA Finerprinting.” Encyclopedia Britannica , 26 Apr. 2018, www.britannica.com/science/DNA-fingerprinting#ref153186. Dror, Itiel E., and Greg Hampikian. “Subjectivity and Bias in Forensic DNA Mixture Interpretation.” Science & Justice, vol. 51, no. 4, 2011, pp. 204–208., doi:10.1016/j.scijus.2011.08.004. Jobling, Mark A., and Peter Gill. “Encoded Evidence: DNA in Forensic Analysis.” Nature Reviews: Genetics, vol. 5, no. 10, Oct. 2004, pp. 739–751., doi:10.1038/nrg1455. Thompson, William C, et al. “How the Probability of a False Positive Affects the Value of DNA Evidence.” Journal of Forensic Sciences, vol. 48, no. 1, Jan. 2003, pp. 1–8., doi:10.1520/jfs2001171.