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The latest activity to be updated on this site is called "Similar Triangles" (Understand similarity to calculate lengths in rotated and reflected triangles.).

So far this activity has been accessed 129 times and 10 people have earned a Transum Trophy for completing it.

Similar Triangles

Understanding similar triangles is crucial for pupils in maths as it lays the foundation for several important mathematical concepts and applications. By learning about similarity, pupils develop the skills needed to calculate unknown lengths and angles in geometric figures that are either rotated or reflected.

Learning about similarity also helps pupils understand the relationships between different shapes and how they can be transformed while still maintaining proportional characteristics. This knowledge is essential for more advanced topics in geometry and trigonometry, as well as in real-world applications such as map scaling, architecture, and engineering.

Moreover, grasping the concept of similar triangles fosters critical thinking skills, problem-solving abilities, and spatial reasoning. It encourages pupils to think logically and analytically when approaching geometric problems and challenges, thus strengthening their overall mathematical proficiency.

Overall, mastering the topic of similar triangles equips pupils with a fundamental understanding of geometric principles that are essential for their mathematical development and future academic success.


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Newsletter

The Transum Newsletter for June 2026 has just been published. Click on the image above to read about the latest developments on this site and try to solve the puzzle of the month. You can read the newsletter online or listen to it by downloading the podcast.

Recent News:

Scientists discover hidden math secret inside Chinese money plant leaves

Scientists have uncovered a hidden mathematical secret inside the leaves of the Chinese money plant: a naturally occurring geometric pattern known as a Voronoi diagram, something typically associated with city planning, computer science, and network design. By mapping tiny pores and looping veins in the plant’s leaves, researchers discovered that the plant organizes itself using the same kind of elegant spatial logic humans use to solve complex distance problems — without ever “measuring” anything. more...

New AI method tackles one of science’s hardest math problems

Penn researchers have developed a smarter AI method for solving notoriously difficult inverse equations, which help scientists uncover hidden causes behind observable effects. By introducing “mollifier layers” that smooth noisy data, they’ve made these calculations more stable and far less computationally demanding. This could transform fields like genetics, where understanding how DNA behaves is key to disease research. more...

Scientists just captured a mysterious quantum “dance” inside superconductors

In a breakthrough experiment, scientists directly imaged how particles pair up in a system that mimics superconductors. Instead of behaving independently, the pairs moved in a synchronized, dance-like pattern—something never predicted before. This suggests a major gap in the classic theory of superconductivity. more...

This donut-shaped discovery just shattered a 150-year math rule

A 150-year-old rule in geometry has been proven wrong. Mathematicians found two different doughnut-shaped surfaces that look identical when measured locally but are actually different overall. For decades, researchers suspected this might be possible but couldn’t prove it—until now. The breakthrough reshapes how mathematicians understand the relationship between local measurements and global form. more...

This simple change stops robot swarms from getting stuck

In crowded environments, more robots don’t always mean faster results—in fact, too many can bring everything to a standstill. Harvard researchers discovered a surprising fix: adding a bit of randomness to how robots move can actually prevent gridlock and boost efficiency. By allowing robots to “wiggle” slightly instead of marching in straight lines, they can slip past each other and keep tasks flowing smoothly. more...

New light trap design supercharges atom-thin semiconductors

Scientists have found a clever way to supercharge ultra-thin semiconductors by reshaping the space beneath them rather than altering the material itself. By placing a single-atom-thick layer of tungsten disulfide over tiny air cavities carved into a crystal, they created miniature “light traps” that dramatically boost brightness and optical effects—up to 20 times stronger emission and 25 times stronger nonlinear signals. These hollow structures, called Mie voids, concentrate light exactly where the material sits, overcoming a major limitation of atomically thin devices. more...

Scientists built the hardest AI test ever and the results are surprising

As AI systems began acing traditional tests, researchers realized those benchmarks were no longer tough enough. In response, nearly 1,000 experts created Humanity’s Last Exam, a massive 2,500-question challenge covering highly specialized topics across many fields. The exam was engineered so that any question solvable by current AI models was removed. Early results show even the most advanced systems still struggle — revealing a surprisingly large gap between AI performance and true expert-level knowledge. more...

Latest Newsletters:

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June 2026

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January 2026

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October's Newsletter :: Podcasts


September 2025

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