{"items":["5f7fcd33672a280018b623bd","5f7fcd33672a280018b623be","5f7fcd33672a280018b623bf"],"styles":{"galleryType":"Columns","groupSize":1,"showArrows":true,"cubeImages":true,"cubeType":"max","cubeRatio":1.7777777777777777,"isVertical":true,"gallerySize":1000,"collageAmount":0,"collageDensity":0,"groupTypes":"1","oneRow":false,"imageMargin":2.5,"galleryMargin":0,"floatingImages":0,"chooseBestGroup":true,"smartCrop":false,"hasThumbnails":false,"enableScroll":true,"isGrid":true,"isSlider":false,"isColumns":false,"isSlideshow":false,"cropOnlyFill":false,"fixedColumns":0,"enableInfiniteScroll":true,"isRTL":false,"minItemSize":50,"rotatingGroupTypes":"","rotatingCubeRatio":"","gallerySliderImageRatio":1.7777777777777777,"numberOfImagesPerRow":3,"numberOfImagesPerCol":1,"groupsPerStrip":0,"borderRadius":0,"boxShadow":0,"gridStyle":0,"mobilePanorama":false,"placeGroupsLtr":false,"viewMode":"preview","thumbnailSpacings":4,"galleryThumbnailsAlignment":"bottom","isMasonry":false,"isAutoSlideshow":false,"slideshowLoop":false,"autoSlideshowInterval":4,"useCustomButton":false,"bottomInfoHeight":0,"titlePlacement":["SHOW_ON_THE_RIGHT","SHOW_BELOW"],"galleryHorizontalAlign":"center","galleryTextAlign":"center","galleryVerticalAlign":"center","scrollSnap":false,"itemClick":"expand","fullscreen":true,"allowSocial":true,"allowDownload":false,"allowTitle":true,"allowDescription":false,"loveButton":true,"loveCounter":false,"videoPlay":"hover","scrollAnimation":"NO_EFFECT","scrollDirection":0,"overlayAnimation":"FADE_IN","arrowsPosition":0,"arrowsSize":23,"watermarkOpacity":40,"watermarkSize":40,"useWatermark":true,"watermarkDock":{"top":"auto","left":"auto","right":0,"bottom":0,"transform":"translate3d(0,0,0)"},"loadMoreAmount":"all","defaultShowInfoExpand":1,"allowTitleExpand":true,"allowDescriptionExpand":true,"allowLinkExpand":true,"expandInfoPosition":0,"allowFullscreenExpand":true,"fullscreenLoop":false,"galleryAlignExpand":"left","addToCartBorderWidth":1,"addToCartButtonText":"","slideshowInfoSize":200,"playButtonForAutoSlideShow":false,"allowSlideshowCounter":false,"hoveringBehaviour":"NEVER_SHOW","thumbnailSize":120,"magicLayoutSeed":1,"imageHoverAnimation":"NO_EFFECT","calculateTextBoxHeightMode":"MANUAL","calculateTextBoxWidthMode":"PERCENT","textBoxHeight":26,"textBoxWidth":200,"textBoxWidthPercent":65,"textImageSpace":10,"textBoxBorderRadius":0,"textBoxBorderWidth":0,"textsVerticalPadding":0,"textsHorizontalPadding":-30,"titleDescriptionSpace":6,"customButtonText":"","customButtonBorderWidth":1,"customButtonBorderRadius":0,"loadMoreButtonText":"","loadMoreButtonBorderWidth":1,"loadMoreButtonBorderRadius":0,"imageInfoType":"ATTACHED_BACKGROUND","itemBorderWidth":0,"itemBorderRadius":0,"itemEnableShadow":false,"itemShadowBlur":20,"itemShadowDirection":135,"itemShadowSize":10,"imageLoadingMode":"BLUR","expandAnimation":"NO_EFFECT","imageQuality":90,"usmToggle":false,"usm_a":0,"usm_r":0,"usm_t":0,"videoSound":false,"videoSpeed":"1","videoLoop":true,"gallerySizeType":"px","gallerySizePx":1000,"allowContextMenu":true,"itemBorderColor":{"themeName":"color_12","value":"rgba(244,210,122,0)"},"galleryLayout":2,"modifiedGallerySize":true,"selectedLayout":"2|bottom|1|max|true|0|true","layoutsVersion":2,"selectedLayoutV2":2,"isSlideshowFont":true,"externalInfoHeight":26,"externalInfoWidth":0.65},"container":{"width":300,"galleryWidth":305,"galleryHeight":1440,"scrollBase":0,"height":null}}

# Teaching Self-Discovery

Anyone would agree that figuring something out on your own is satisfying, and often preferable to being told what to do. Some concepts such as proportion are difficult to teach. That is where ARTriangles provide a creative environment for discovering geometric proportion with no instruction necessary.

Arranging these triangles into inventive designs helps you discover their self-organizing nature and begin to glimpse their unique properties.

ARTriangles' limitless designs challenge the imagination. Anyone can come up with something original and creative, whether simple or complex.

Group activities bring shared delight and discovery. For example, each student can take turns placing triangles to build a design and watch it develop in an unpredictable way. Or the group can work toward a goal such as a frog, butterfly, or flower.

Anyone who discovers the logic of fractals contained in ARTriangles is opening the door to a mathematical beauty that has been treasured through the ages by those fortunate enough to experience the Golden Proportion. With no need of equations to explain it, students are soon prepared to appreciate the geometrical qualities and mathematical equations that underly it.