Why did Tinkertoy rods come in different lengths?

Tinkertoy rods came in different lengths so that a diagonal connection could meet the ends of two shorter sides. The lengths worked with the holes in the wooden hubs: choosing a longer stick was part of a geometric system, not simply a way to make a taller tower. Charles H. Pajeau’s 1914 patent explains that system through a sequence of triangles.^[1]

The Strong museum identifies Pajeau and Robert Petit as the creators of Tinkertoy, combining sticks with drilled wooden wheels. The colored pieces familiar from later sets came afterward; the museum places their arrival in the 1950s. The Junior set pictured above shows that recognizable assortment, but it is not evidence of what a package contained in 1914.^[2][3]

The diagonal becomes the next side

Pajeau preferred holes spaced 45 degrees apart around a disk. Two equal connections meeting at a right angle could therefore be joined by a longer diagonal. In Figure 3, that longer side becomes a short side of the next, larger triangle. Repeating the relationship produces a family of compatible lengths instead of an arbitrary collection of sticks.^[1]

Here is a numerical illustration, not a measurement of a commercial set. Imagine the two equal distances between hub centers are each 10 units. The diagonal distance is the square root of 10 squared plus 10 squared: about 14.14 units. Use that diagonal as each short side of the next triangle and its new diagonal is 20 units. That explains the repeated multiplier of roughly 1.414.^[1]

A stick is shorter than the connection it makes

Those numbers describe distances between hub centers. A rod ends inside a socket before reaching the center of the disk. Pajeau explicitly allowed for that gap when choosing actual rod lengths. Multiplying the length of one loose stick by 1.414 therefore does not, by itself, give the exact length of the next stick. The hubs supply part of every connection.^[1]

The patent also addresses the awkward final corner. Once two sides are connected, their free ends cannot always slide straight into the last hub at the same time. Slits in the rod tips let them compress during insertion and spring outward to grip the sockets. Figure 5 shows the temporary spreading needed to close the triangle; this explains the design, rather than recommending force on an old set.^[1]

Seen this way, the round hubs do two jobs: they set the direction of each connection and contribute to its effective length. The rods provide the remaining span and a yielding joint. Lincoln Logs used notches to register crossing pieces; Tinkertoy used angles and compatible spans to make a framework close. That is the useful detail hidden in the familiar pile of parts.^[1][4]

What did you build with Tinkertoys: something from the plans or a machine of your own?