# arithmetic – The Pleasure of Hexasect

[ad_1]

This geometric development problem is

a set of parts to be positioned so as,

$begingroup

def s #1{{ smallsf #1 }}

def AB { overline {s{AB}} }

def line #1{{ small overleftrightarrow {s{#1}} }}

$

dividing line phase $AB$ of size **6**

into 6 subsegments, every of size **1**.

*hexasect* – transitive

verb – to divide into 6 equal elements

*How can $AB$ be hexasected by inserting 5 circles and seven traces
that produce simply 1 lines-only node?*

**Development tips**

•

Circles and contours are positioned sequentially,

in any order that accords with *nodes* that exist at instances of placement.

•

A circle could also be positioned the place a node exists for the circle’s heart.

•

A line could also be positioned the place it crosses a minimum of two current nodes.

•

*Nodes* are endpoints **A** and **B** in addition to

intersections amongst circles, traces and/or $AB$.

•

A *lines-only node* is an intersection of *traces* within the accomplished resolution.

No circles go by means of a lines-only node.

(Nodes alongside $AB$ are ineligible as a result of $AB$

is technically a *phase*, not a *line*.)

**Instance**

*quadrisect* – transitive

verb – to divide into 4 equal elements

A special $AB$, of size 4, might be quadrisected

by inserting 4 circles and 6 traces

that produce simply 1 lines-only node.

• Step 1

locations circles centered at nodes **A** and **B**.

These circles’ intersections produce nodes **C** and **D**.

• Step 2

locations line $line{BC}$ and a circle centered at **C**,

whose intersection produces node **E**,

and locations $line{CD}$,

whose intersection with $AB$ produces node **F**.

• Step 3

locations a circle centered at **E**.

This circle’s intersection with $line{BC}$

produces node **G**.

• Step 4

locations traces $line{AD}$ and $line{FG}$,

whose intersection produces node **H**.

• Step 5

completes this quadrisection

by inserting traces $line{CH}$ and $line{DG}$.

The specified lines-only node is **H**.

$endgroup$

[ad_2]