How does a periscope work? How does light travel through a periscope? How can you make a periscope yourself? Simon answers these questions in the video:

Also tried to trace the motion of light inside the periscope using a laser beam:

How does a periscope work? How does light travel through a periscope? How can you make a periscope yourself? Simon answers these questions in the video:

Also tried to trace the motion of light inside the periscope using a laser beam:

Simon got a belated birthday present from his Russian grandparents, something he had dreamed about for months: the Magformers Sky Track set, sort of a monorail that allows Simon the shuttle to ride vertically and upside down, seemingly defying gravity:

Combining the Sky Track with a domino chain reaction:

Simon building the AND logic gate with dominos:

Simon took the Sky Track along when visiting an older friend in Amsterdam and it had great success. We generally see Simon open up more to playing together and just having genuine childlike fun instead of having continuous scruples about waisting time and the need to be working on his science and programming projects without interruption.

Although Simon doesn’t have the Magformers Dinosaur Set, he does have all the pieces (he collects the set using the pieces from other sets). It’s great fun to be able to look up the dinos and the instructions in the Magformers online pdf books and bring them back to life:

We also read up on how these dinos lived in the encyclopaedias.

Simon prepared 100 2D shapes to make over 100 solids yesterday. He started with the easy one that he had built hundreds of times before, when he was much younger (like the Platonic Solids and some of the Archimedean Solids and anti-prisms), but then went on to less familiar categories, like elongated and gyroelongated cupolae and dipyramids! Never heard of a Gyrobifastigium? Take a look below!

*Dodecahedron*

*Icosahedron*

*Cuboctahedron*

*Small Rhombicuboctahedron* (by expanding a cube)

*Icosidodecahedron*

Simon didn’t build a snub cube (“is a real challenge and has two different versions that are mirror images of each other”). Nor did he make a truncated dodecahedron (as he has no decagons), nor a truncated icosahedron (doesn’t have 20 hexagons). “If you slice the corners off of an icosahedron, you get a truncated icosahedron also known as a… football!” The 62-sided rhombicosidodecahedron he had already made many times before, we’ll post an old photo later.

And then came the antiprisms:

*A square antiprism – two squares connected with a band of equilateral triangles*

*A pentagonal antiprism*

And the elongated shapes:

*Pentagonal cupola (half a cantellated dodecahedron); there is no hexagonal cupola*

*Pentagonal rotunda (half of an icosidodecahedron)*

*Gyroelongated triangular pyramid*

*Gyroelongated square pyramid*

“If you gyroelongate a pentagonal pyramid, it looks like an icosahedron, but isn’t quite that”:

*Gyroelongated pentagonal pyramid*

*Elongated square dipyramid*

*Elongated triangular cupola*

*Gyroelongated triangular cupola*

*Gyrobifastigium* (there it is, you found it!)

*Square orthobicupola*

*Pentagonal orthobicupola* (above) *and its twisted variant – pentagonal gyrobicupola* (below), looking like a UFO

Simon explains how to to turn Platonic Solids into Archimedean Solids, using truncation and rectification.

Simon explains how to convert Platonic Solids to Archimedean Solids and builds a Rhombicosidodecahedron from 62 Magformers pieces.

Magformers did not sponsor these videos. In fact, we’ve been sponsoring Magformers 🙂

Its Highness Magformers S.T.E.A.M. Master Set, Simon’s long aspired gift for Sinterklaas (the biggest holiday of the year for the Dutch) and what he built with it. The set mainly focuses on studying the way light is reflected by mirrors (such as in a camera or a periscope).

Simon and Neva had been singing the traditional Sinterklaas songs (with new non-racist and non-violent lyrics) every evening and finding small gifts in their shoes every morning for two weeks, this whole roller-coaster culminating in the Sinterklaas “pakjesavond” (the night of the presents) in early December with the extended family in Utrecht, where the “real gifts” were secretly delivered by Sint Nicolaas and his helpers. In the picture above, Simon is reading one of the poems (there are poems accompanying every gift). Sinterklaas was up all night last night writing poems.

At home unpacking the gift.

Simon is trying to write a program for Sphere Morphing in Processing, first making a test code in p5.js (available here: https://alpha.editor.p5js.org/simontiger/sketches/S1zcwevkz)

In the video below, Simon is explaining the challenge using Magformers triangles:

Unfortunately, the test code doesn’t quite work yet: Simon is getting three infinite triangles around the circle.

Simon built “the shadow of a 4D object” during math class, inspired by the Royal Institution’s video Four Dimensional Maths: Things to See and Hear in the Fourth Dimension with Matt Parker. Simon loved the video and watched it twice. We had come across similar thought experiments while reading a book by Jacob Perelman, a Russian mathematician, where the 4th dimension was visualized as the time dimension and the objects sliding along that 4th axis would appear and disappear in our 3D world just like 3D objects would appear as their cross sections if they were observed by 2D creatures. Here is how Simon visualized it.

The first drawing is of a 3D object the way it actually looks when passing through a 2D world:

And this is what the inhabitants of the 2D world (unable to see in 3D) see – a sequence of sections of the 3D object. Similarly, we (unable to see in 4D) only see sequences of 3D sections of the 4D objects passing our world. Maybe, everything we see around us are such sections of much more complex objects as they are moving through time. “Maybe, we’re just 3D shadows of 4D objects”, says Simon.

Simon pulled out his old Magformers Pythagoras set and this time around, he really nailed all the tasks independently. The set offers a variety of puzzles to “prove” the Pythagorean theorem and apply it to other shapes (even 3D!), as well as teaches several more tricks (such as the ratios between the areas of similar triangles or the areas of parallelograms).

Chinese square Proof:

Area of Parallelograms:

Applying Pythagorean theorem to other shapes:

Extended theorem by the Greek mathematician Pappus:

Areas of Similar Triangles:

More of Pythagorean theorem with various shapes:

Puzzles: